Deep learning techniques for generating magnetic resonance images from spatial frequency data

ABSTRACT

Techniques for generating magnetic resonance (MR) images of a subject from MR data obtained by a magnetic resonance imaging (MRI) system, the techniques include: obtaining input MR spatial frequency data obtained by imaging the subject using the MRI system; generating an MR image of the subject from the input MR spatial frequency data using a neural network model comprising: a pre-reconstruction neural network configured to process the input MR spatial frequency data; a reconstruction neural network configured to generate at least one initial image of the subject from output of the pre-reconstruction neural network; and a post-reconstruction neural network configured to generate the MR image of the subject from the at least one initial image of the subject.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Application Ser. No. 62/818,148, Attorney Docket No.O0354.70038US00, filed Mar. 14, 2019, and titled “DEEP LEARNINGTECHNIQUES FOR MOTION COMPENSATION IN MAGNETIC RESONANCE IMAGING,” U.S.Provisional Application Ser. No. 62/820,119, Attorney Docket No.“O0354.70039US00”, filed Mar. 18, 2019, and titled “END-TO-END LEARNABLEMR IMAGE RECONSTRUCTION”, and U.S. Provisional Application Ser. No.62/926,890, Attorney Docket No. O0354.70049US00, filed Oct. 28, 2019,and titled “SELF ENSEMBLING TECHNIQUES FOR DEEP LEARNING BASED MRIRECONSTRUCTION”, each of which is incorporated by reference in itsentirety herein.

FIELD

The present disclosure relates generally to generating magneticresonance (MR) images from input MR spatial frequency data and, morespecifically, to machine learning (e.g., deep learning) techniques forprocessing input MR spatial frequency data to produce MR images.

BACKGROUND

Magnetic resonance imaging (MRI) provides an important imaging modalityfor numerous applications and is widely utilized in clinical andresearch settings to produce images of the inside of the human body. MRIis based on detecting magnetic resonance (MR) signals, which areelectromagnetic waves emitted by atoms in response to state changesresulting from applied electromagnetic fields. For example, nuclearmagnetic resonance (NMR) techniques involve detecting MR signals emittedfrom the nuclei of excited atoms upon the re-alignment or relaxation ofthe nuclear spin of atoms in an object being imaged (e.g., atoms in thetissue of the human body). Detected MR signals may be processed toproduce images, which in the context of medical applications, allows forthe investigation of internal structures and/or biological processeswithin the body for diagnostic, therapeutic and/or research purposes.

MRI provides an attractive imaging modality for biological imaging dueto its ability to produce non-invasive images having relatively highresolution and contrast without the safety concerns of other modalities(e.g., without needing to expose the subject to ionizing radiation, suchas x-rays, or introducing radioactive material into the body).Additionally, MRI is particularly well suited to provide soft tissuecontrast, which can be exploited to image subject matter that otherimaging modalities are incapable of satisfactorily imaging. Moreover, MRtechniques are capable of capturing information about structures and/orbiological processes that other modalities are incapable of acquiring.

SUMMARY

Some embodiments provide for a method for generating magnetic resonance(MR) images of a subject from MR data obtained by a magnetic resonanceimaging (MRI) system. The method comprises: obtaining input MR spatialfrequency data obtained by imaging the subject using the MRI system;generating an MR image of the subject from the input MR spatialfrequency data using a neural network model comprising: apre-reconstruction neural network configured to process the input MRspatial frequency data; a reconstruction neural network configured togenerate at least one initial image of the subject from output of thepre-reconstruction neural network; and a post-reconstruction neuralnetwork configured to generate the MR image of the subject from the atleast one initial image of the subject.

Some embodiments provide for a magnetic resonance imaging (MRI) system,comprising: a magnetics system having a plurality of magneticscomponents to produce magnetic fields for performing MRI; and at leastone processor configured to perform: obtaining input MR spatialfrequency data obtained by imaging the subject using the MRI system;generating an MR image of the subject from the input MR spatialfrequency data using a neural network model comprising: apre-reconstruction neural network configured to process the input MRspatial frequency data; a reconstruction neural network configured togenerate at least one initial image of the subject from output of thepre-reconstruction neural network; and a post-reconstruction neuralnetwork configured to generate the MR image of the subject from the atleast one initial image of the subject.

Some embodiments provide for a system comprising at least one processorconfigured to perform: obtaining input MR spatial frequency dataobtained by imaging the subject using the MRI system; generating an MRimage of the subject from the input MR spatial frequency data using aneural network model comprising: a pre-reconstruction neural networkconfigured to process the input MR spatial frequency data; areconstruction neural network configured to generate at least oneinitial image of the subject from output of the pre-reconstructionneural network; and a post-reconstruction neural network configured togenerate the MR image of the subject from the at least one initial imageof the subject.

Some embodiments provide for at least one non-transitory computerreadable storage medium storing processor-executable instructions that,when executed by at least one processor, cause the at least oneprocessor to perform a method for generating magnetic resonance (MR)images of a subject from MR data obtained by a magnetic resonanceimaging (MRI) system. The method comprises: obtaining input MR spatialfrequency data obtained by imaging the subject using the MRI system;generating an MR image of the subject from the input MR spatialfrequency data using a neural network model comprising: apre-reconstruction neural network configured to process the input MRspatial frequency data; a reconstruction neural network configured togenerate at least one initial image of the subject from output of thepre-reconstruction neural network; and a post-reconstruction neuralnetwork configured to generate the MR image of the subject from the atleast one initial image of the subject.

Some embodiments provide a method for generating magnetic resonance (MR)images of a subject from MR data obtained by a magnetic resonanceimaging (MRI) system. The method comprising: obtaining first input MRdata obtained by imaging the subject using the MRI system; obtainingsecond input MR data obtained by imaging the subject using the MRIsystem; generating a first set of one or more MR images from the firstinput MR data; generating a second set of one or more MR images from thesecond input MR data; aligning the first set of MR images and the secondset of MR images using a neural network model to obtain aligned firstand second sets of MR images, the neural network model comprising afirst neural network and a second neural network, the aligningcomprising: estimating, using the first neural network, a firsttransformation between the first set of MR images and the second set ofMR images; generating a first updated set of MR images from the secondset of MR images using the first transformation; estimating, using thesecond neural network, a second transformation between the first set ofMR images and the first updated set of MR images; and aligning the firstset of MR images and the second set of MR images at least in part byusing the first transformation and the second transformation; combiningthe aligned first and second sets of MR images to obtain a combined setof one or more MR images; and outputting the combined set of one or moreMR images.

Some embodiments at least one non-transitory computer-readable storagemedium storing processor-executable instructions that, when executed byat least one processor, cause the at least one processor to perform amethod for generating magnetic resonance (MR) images of a subject fromMR data obtained by a magnetic resonance imaging (MRI) system. Themethod comprises: obtaining first input MR data obtained by imaging thesubject using the MRI system; obtaining second input MR data obtained byimaging the subject using the MRI system; generating a first set of oneor more MR images from the first input MR data; generating a second setof one or more MR images from the second input MR data; aligning thefirst set of MR images and the second set of MR images using a neuralnetwork model to obtain aligned first and second sets of MR images, theneural network model comprising a first neural network and a secondneural network, the aligning comprising: estimating, using the firstneural network, a first transformation between the first set of MRimages and the second set of MR images; generating a first updated setof MR images from the second set of MR images using the firsttransformation; estimating, using the second neural network, a secondtransformation between the first set of MR images and the first updatedset of MR images; and aligning the first set of MR images and the secondset of MR images at least in part by using the first transformation andthe second transformation; combining the aligned first and second setsof MR images to obtain a combined set of one or more MR images; andoutputting the combined set of one or more MR images.

Some embodiments provide for a magnetic resonance imaging (MRI) system,comprising: a magnetics system having a plurality of magneticscomponents to produce magnetic fields for performing MRI; and at leastone processor configured to perform: obtaining first input MR data byimaging the subject using the MRI system; obtaining second input MR databy imaging the subject using the MRI system; generating a first set ofone or more MR images from the first input MR data; generating a secondset of one or more MR images from the second input MR data; aligning thefirst set of MR images and the second set of MR images using a neuralnetwork model to obtain aligned first and second sets of MR images, theneural network model comprising a first neural network and a secondneural network, the aligning comprising: estimating, using the firstneural network, a first transformation between the first set of MRimages and the second set of MR images; generating a first updated setof MR images from the second set of MR images using the firsttransformation; estimating, using the second neural network, a secondtransformation between the first set of MR images and the first updatedset of MR images; and aligning the first set of MR images and the secondset of MR images at least in part by using the first transformation andthe second transformation; combining the aligned first and second setsof MR images to obtain a combined set of one or more MR images; andoutputting the combined set of one or more MR images.

Some embodiments provide for a system, comprising at least one processorconfigured to perform: obtaining first input MR data obtained by imagingthe subject using the MRI system; obtaining second input MR dataobtained by imaging the subject using the MRI system; generating a firstset of one or more MR images from the first input MR data; generating asecond set of one or more MR images from the second input MR data;aligning the first set of MR images and the second set of MR imagesusing a neural network model to obtain aligned first and second sets ofMR images, the neural network model comprising a first neural networkand a second neural network, the aligning comprising: estimating, usingthe first neural network, a first transformation between the first setof MR images and the second set of MR images; generating a first updatedset of MR images from the second set of MR images using the firsttransformation; estimating, using the second neural network, a secondtransformation between the first set of MR images and the first updatedset of MR images; and aligning the first set of MR images and the secondset of MR images at least in part by using the first transformation andthe second transformation; combining the aligned first and second setsof MR images to obtain a combined set of one or more MR images; andoutputting the combined set of one or more MR images.

Some embodiments provide for a method for generating magnetic resonance(MR) images of a subject from MR data obtained by a magnetic resonanceimaging (MRI) system, the method comprising: obtaining input MR dataobtained by imaging the subject using the MRI system; generating aplurality of transformed input MR data instances by applying arespective first plurality of transformations to the input MR data;generating a plurality of MR images from the plurality of transformedinput MR data instances and the input MR data using a non-linear MRimage reconstruction technique; generating an ensembled MR image fromthe plurality of MR images at least in part by: applying a secondplurality of transformations to the plurality of MR images to obtain aplurality of transformed MR images; and combining the plurality oftransformed MR images to obtain the ensembled MR image; and outputtingthe ensembled MR image.

Some embodiments provide for at least one non-transitorycomputer-readable storage medium storing processor-executableinstructions that, when executed by at least one processor, cause the atleast one processor to perform a method for generating magneticresonance (MR) images of a subject from MR data obtained by a magneticresonance imaging (MRI) system, the method comprising: obtaining inputMR data obtained by imaging the subject using the MRI system; generatinga plurality of transformed input MR data instances by applying arespective first plurality of transformations to the input MR data;generating a plurality of MR images from the plurality of transformedinput MR data instances and the input MR data using a non-linear MRimage reconstruction technique; generating an ensembled MR image fromthe plurality of MR images at least in part by: applying a secondplurality of transformations to the plurality of MR images to obtain aplurality of transformed MR images; and combining the plurality oftransformed MR images to obtain the ensembled MR image; and outputtingthe ensembled MR image.

Some embodiments provide for at least one a magnetic resonance imaging(MRI) system configured to capture a magnetic resonance (MR) image, theMRI system comprising: a magnetics system having a plurality ofmagnetics components to produce magnetic fields for performing MRI; andat least one processor configured to perform: obtaining input MR dataobtained by imaging the subject using the MRI system; generating aplurality of transformed input MR data instances by applying arespective first plurality of transformations to the input MR data;generating a plurality of MR images from the plurality of transformedinput MR data instances and the input MR data using a non-linear MRimage reconstruction technique generating an ensembled MR image from theplurality of MR images at least in part by: applying a second pluralityof transformations to the plurality of MR images to obtain a pluralityof transformed MR images; and combining the plurality of transformed MRimages to obtain the ensembled MR image; and outputting the ensembled MRimage.

Some embodiments provide for a system, comprising at least one processorconfigured to perform: obtaining input MR data obtained by imaging thesubject using the MRI system; generating a plurality of transformedinput MR data instances by applying a respective first plurality oftransformations to the input MR data; generating a plurality of MRimages from the plurality of transformed input MR data instances and theinput MR data using a non-linear MR image reconstruction technique;generating an ensembled MR image from the plurality of MR images atleast in part by: applying a second plurality of transformations to theplurality of MR images to obtain a plurality of transformed MR images;and combining the plurality of transformed MR images to obtain theensembled MR image; and outputting the ensembled MR image.

Some embodiments provide for a method for generating magnetic resonance(MR) images from MR data obtained by a magnetic resonance imaging (MRI)system comprising a plurality of RF coils configured to detect RFsignals. The method comprising: obtaining a plurality of input MRdatasets obtained by the MRI system to image a subject, each of theplurality of input MR datasets comprising spatial frequency data andobtained using a respective RF coil in the plurality of RF coils;generating a respective plurality of MR images from the plurality ofinput MR datasets by using an MR image reconstruction technique;estimating, using a neural network model, a plurality of RF coilprofiles corresponding to the plurality of RF coils; generating an MRimage of the subject using the plurality of MR images and the pluralityof RF coil profiles; and outputting the generated MR image.

Some embodiments provide for a magnetic resonance imaging (MRI) system,comprising: a magnetics system having a plurality of magneticscomponents to produce magnetic fields for performing MRI, the magneticssystem comprising a plurality of RF coils configured to detect MRsignals; and at least one processor configured to perform: obtaining aplurality of input MR datasets obtained by the MRI system to image asubject, each of the plurality of input MR datasets comprising spatialfrequency data and obtained using a respective RF coil in the pluralityof RF coils; generating a respective plurality of MR images from theplurality of input MR datasets by using an MR image reconstructiontechnique; estimating, using a neural network model, a plurality of RFcoil profiles corresponding to the plurality of RF coils; generating anMR image of the subject using the plurality of MR images and theplurality of RF coil profiles; and outputting the generated MR image.

Some embodiments provide for a system comprising at least one processorconfigured to perform: obtaining a plurality of input MR datasetsobtained by an MRI system to image a subject, each of the plurality ofinput MR datasets comprising spatial frequency data and obtained using arespective RF coil in a plurality of RF coils of the MRI system;generating a respective plurality of MR images from the plurality ofinput MR datasets by using an MR image reconstruction technique;estimating, using a neural network model, a plurality of RF coilprofiles corresponding to the plurality of RF coils; generating an MRimage of the subject using the plurality of MR images and the pluralityof RF coil profiles; and outputting the generated MR image.

Some embodiments provide for at least one non-transitory computerreadable storage medium storing processor-executable instructions that,when executed by at least one processor, cause the at least oneprocessor to perform a method for generating magnetic resonance (MR)images of a subject from MR data obtained by a magnetic resonanceimaging (MRI) system having a plurality of RF coils configured to detectMR signals. The method comprises: obtaining a plurality of input MRdatasets obtained by the MRI system to image a subject, each of theplurality of input MR datasets comprising spatial frequency data andobtained using a respective RF coil in the plurality of RF coils;generating a respective plurality of MR images from the plurality ofinput MR datasets by using an MR image reconstruction technique;estimating, using a neural network model, a plurality of RF coilprofiles corresponding to the plurality of RF coils; generating an MRimage of the subject using the plurality of MR images and the pluralityof RF coil profiles; and outputting the generated MR image.

Some embodiments provide for a method for generating magnetic resonance(MR) images from MR data obtained by a magnetic resonance imaging (MRI)system comprising a plurality of RF coils configured to detect RFsignals. The method comprises: obtaining a plurality of input MRdatasets obtained by the MRI system to image a subject, each of theplurality of input MR datasets comprising spatial frequency data andobtained using a respective RF coil in the plurality of RF coils;generating, from the plurality of input MR datasets and using ageometric coil compression technique, a plurality of virtual input MRdatasets having fewer input MR datasets than the first plurality ofinput MR datasets; generating a plurality of MR images from theplurality of virtual input MR datasets by applying a neural network MRimage reconstruction technique to the plurality of virtual input MRdatasets; generating an MR image of the subject by combining theplurality of MR images; and outputting the generated MR image.

Some embodiments provide for a magnetic resonance imaging (MRI) system,comprising: a magnetics system having a plurality of magneticscomponents to produce magnetic fields for performing MRI, the magneticssystem comprising a plurality of RF coils configured to detect MRsignals; and at least one processor configured to perform: obtaining aplurality of input MR datasets obtained by the MRI system to image asubject, each of the plurality of input MR datasets comprising spatialfrequency data and obtained using a respective RF coil in the pluralityof RF coils; generating, from the plurality of input MR datasets andusing a geometric coil compression technique, a plurality of virtualinput MR datasets having fewer input MR datasets than the firstplurality of input MR datasets; generating a plurality of MR images fromthe plurality of virtual input MR datasets by applying a neural networkMR image reconstruction technique to the plurality of virtual input MRdatasets; generating an MR image of the subject by combining theplurality of MR images; and outputting the generated MR image.

The foregoing is a non-limiting summary of the invention, which isdefined by the attached claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and embodiments of the disclosed technology will bedescribed with reference to the following figures. It should beappreciated that the figures are not necessarily drawn to scale.

FIG. 1 is a diagram illustrating various types of processing performedon data collected by an MRI system while imaging a subject to generatean MR image of the subject.

FIG. 2A is a diagram illustrating processing performed by a neuralnetwork model on data collected by an MRI system while imaging a subjectto generate an MR image of the subject, in accordance with someembodiments of the technology described herein.

FIG. 2B is a diagram of illustrative components of thepre-reconstruction neural network part of the neural network model ofFIG. 2A, in accordance with some embodiments of the technology describedherein.

FIG. 2C is a diagram of illustrative components of thepost-reconstruction neural network part of the neural network model ofFIG. 2A, in accordance with some embodiments of the technology describedherein.

FIG. 2D is a flowchart of an illustrative process for generating an MRimage from input MR spatial frequency data, in accordance with someembodiments of the technology described herein.

FIG. 3A is a diagram of an illustrative of architecture of an exampleneural network model for generating MR images from input MR spatialfrequency data, in accordance with some embodiments of the technologydescribed herein.

FIG. 3B is a diagram of one type of architecture of a block of theneural network model of FIG. 3A, in accordance with some embodiments ofthe technology described herein.

FIG. 3C is a diagram of an illustrative architecture of a dataconsistency block, which may be part of the block shown in FIG. 3B, inaccordance with some embodiments of the technology described herein.

FIG. 3D is a diagram of an illustrative architecture of a convolutionalneural network block, which may be part of the block shown in FIG. 3B,in accordance with some embodiments of the technology described herein.

FIG. 3E is a diagram of another type of architecture of a block of theneural network model of FIG. 3A, in accordance with some embodiments ofthe technology described herein.

FIG. 4A illustrates the architecture of an example convolutional neuralnetwork block having a “U” structure and an average pooling layer, whichblock may be part of the pre-reconstruction neural network model, inaccordance with some embodiments of the technology described herein.

FIG. 4B illustrates a specific example of the architecture of an exampleconvolutional neural network block shown in FIG. 4A, in accordance withsome embodiments of the technology described herein.

FIG. 4C illustrates the architecture of an example convolutional neuralnetwork block having a “U” structure and a spectral unpooling layer,which block may be part of the pre-reconstruction neural network model,in accordance with some embodiments of the technology described herein.

FIG. 4D illustrates the architecture of an example spectral unpoolinglayer, in accordance with some embodiments of the technology describedherein.

FIGS. 5A-5C show an illustrative diagram of a process for generatingtraining data from MR images for training the neural network modelsdescribed herein, in accordance with some embodiments of the technologydescribed herein.

FIG. 6 is a diagram of an example neural-network based architecture foraligning one or more MR images, in accordance with some embodiments ofthe technology described herein.

FIG. 7 is a diagram of the architecture of an illustrative neuralnetwork for aligning one or more MR images, in accordance with someembodiments of the technology described herein.

FIG. 8A is a flowchart of an illustrative process 800 for aligning oneor more MR images, in accordance with some embodiments of the technologydescribed herein.

FIG. 8B is a flowchart of an illustrative implementation of act 850 ofprocess 800 of FIG. 8B, in accordance with some embodiments of thetechnology described herein.

FIG. 9 illustrates a block diagram of an example pipeline for motioncorrection, in accordance with some embodiments of the technologydescribed herein.

FIG. 10 is a flowchart of an illustrative process 1000 for generatingtraining data to train a neural network for aligning one or more images,in accordance with some embodiments of the technology described herein.

FIG. 11A illustrates example motion-corrupted MR images of a patient'sbrain.

FIG. 11B illustrates the result of applying the neural networktechniques described herein to correct for motion in the MR images ofFIG. 11A, in accordance with some embodiments of the technologydescribed herein.

FIG. 12A illustrates another example of motion-corrupted MR images of apatient's brain.

FIG. 12B illustrates the result of applying the neural networktechniques described herein to correct for motion in the MR images ofFIG. 12A, in accordance with some embodiments of the technologydescribed herein.

FIG. 13A illustrates motion-corrupted MR images, the motion occurringalong the z-direction (out of the plane of the images).

FIG. 13B illustrates the result of applying the neural networktechniques described herein to correct for motion in the MR images ofFIG. 13A, in accordance with some embodiments of the technologydescribed herein.

FIG. 14A illustrates MR images having no motion-corruption.

FIG. 14B illustrates the result of applying the neural networktechniques described herein to the MR images of FIG. 14A, which showsthat no motion is detected, no correction in performed, in accordancewith some embodiments of the technology described herein.

FIG. 15 is a diagram illustrating a self-ensembling approach tonon-linear MR image reconstruction, in accordance with some embodimentsof the technology described herein.

FIG. 16 is a flowchart of an illustrative process 1600 for performingnon-linear MR image reconstruction using self ensembling, in accordancewith some embodiments of the technology described herein.

FIGS. 17A and 17B show example MR images of a subject's brain obtainedwithout self-ensembling and with self-ensembling, respectively, inaccordance with some embodiments of the technology described herein.

FIGS. 18A and 18B show example MR images of a subject's brain obtained(by different RF coils) without self-ensembling and withself-ensembling, respectively, in accordance with some embodiments ofthe technology described herein.

FIGS. 19A and 19B show example MR images of a subject's brain obtainedwithout self-ensembling and with self-ensembling, respectively, inaccordance with some embodiments of the technology described herein.

FIG. 20A is a flowchart of an illustrative process 2000 for generatingan MR image from input MR spatial frequency data collected by multipleRF coils, the process including estimate RF coil profiles using a neuralnetwork, in accordance with some embodiments of the technology describedherein.

FIG. 20B is an illustrate example architecture of a neural network forestimating RF coil profiles, in accordance with some embodiments of thetechnology described herein.

FIGS. 20C, 20D, 20E, 20F, 20G, and 20H illustrate performance of theneural network coil profile estimation techniques described hereinrelative to conventional parallel imaging techniques.

FIG. 21 is a flowchart of an illustrative process 2100 for generating anMR image using geometric coil compression from data obtained by multiplephysical RF coils, in accordance with some embodiments of the technologydescribed herein.

FIG. 22 is a schematic illustration of a low-field MRI system, inaccordance with some embodiments of the technology described herein.

FIG. 23 illustrates a bi-planar permanent magnet configuration for a B₀magnet that may be part of the low-field system of FIG. 22, inaccordance with some embodiments of the technology described herein.

FIGS. 24A and 24B illustrate views of a portable MRI system, inaccordance with some embodiments of the technology described herein.

FIG. 25A illustrates a portable MRI system performing a scan of thehead, in accordance with some embodiments of the technology describedherein.

FIG. 25B illustrates a portable MRI system performing a scan of theknee, in accordance with some embodiments of the technology describedherein.

FIG. 26 is a diagram of an illustrative computer system on whichembodiments described herein may be implemented.

DETAILED DESCRIPTION

Conventional techniques for processing MRI data to generate MR images ofpatients involve applying different computational tools to performdifferent tasks part of the processing pipeline for generating MR imagesfrom the MRI data. For example, as shown in FIG. 1, the processingpipeline may involve performing various pre-processing, reconstruction,and post-processing tasks on data acquired by an MRI system. Thepre-processing tasks may include sorting and filtering of data,correcting the data for motion, and suppressing RF artefacts (e.g.,external RF interference generated by any device(s) external to the MRIsystem, internal RF interference generated by any component(s) of theMRI system outside of its imaging region, and noise generated by thereceive circuitry of the MRI system) in the data. After pre-processing,the pipeline may involve reconstructing MR images from the pre-processeddata using linear methods (e.g., gridding, principle components analysis(PCA), sensitivity encoding (SENSE), generalized autocalibrating partialparallel acquisition (GRAPPA) or non-linear methods (e.g., compressedsensing, deep learning)). Next, the resulting images may be postprocessed to perform retrospective motion correction, artefact removal,denoising, intensity correction, and/or image enhancement.

The inventors have appreciated that a fundamental limitation of suchconventional MRI data processing techniques is that each of the tasks inthe processing pipeline is tacked individually. Even though performanceof the tasks is sequenced, solving each such task individually canresult in loss of information at intermediate stages. Moreover, featuresthat can be mutually exploited in multiple stages may be missed. As aresult, the performance of the overall pipeline is sub-optimal resultingin lower quality and lower-SNR images, especially in settings (e.g.,low-field MRI, undersampled data) where the sensor data is noisy andincomplete.

To address shortcomings of conventional MRI processing pipelines, theinventors have developed a unified deep-learning processing pipeline forprocessing MRI data to generate MR images of patients. The deep learningprocessing pipeline developed by the inventors involves using multipleneural networks to perform different pipeline tasks. Examples of suchtasks include removing artefacts (e.g., interference, noise, corruptedreadout lines) from input MR spatial frequency data, reconstructingimages from the input MR spatial frequency data, combining MR imagesgenerated from data collected by different RF coils, aligning sets of MRimages to one another to compensate for patient motion, combiningaligned sets of MR images to increase the image signal to noise (SNR),correcting for inhomogeneous intensity variations. In some embodiments,at least some (e.g., all) of these tasks may be performed by respectiveneural networks.

In some embodiments, the neural networks in the processing pipeline maybe jointly trained. In this way, parameters of neural networks forperforming different tasks (e.g., interference removal, RF coil profileestimation, reconstruction, and motion correction) may be optimizedjointly using a common set of training data and using a common objectivemetric. In some embodiments, the common objective metric may be aweighted combination of loss functions for learning parameters of theneural networks in the deep learning processing pipeline. Each of theneural networks in the pipeline may be trained to perform a respectivetask and the common objective metric may include one or more lossfunction (e.g., as part of the weighted combination) for the respectivetask. Examples of such loss functions are provided herein.

This “end-to-end” deep learning processing pipeline allows anyimprovements made in individual earlier processing stages to propagateto and be used by subsequent processing stages in the pipeline. As aresult, the quality and SNR of MR images generated by the deep learningpipeline is higher than that produced by conventional processingpipelines, which is an improvement in MRI technology. In addition, sinceneural network calculations may be performed efficiently usingspecialized hardware (e.g., one or more graphics processing units(GPUs)), these calculations may be offloaded to such hardware freeing upresources of other onboard processors to perform different tasks—theoverall load on the CPUs is reduced. This is a benefit that cannot beachieved using conventional pipelines as many of the algorithms used inconventional pipelines (e.g., compressed sensing) are not designed forefficient implementation on GPUs. Thus, the techniques described hereinalso provide an improvement to computing technology.

Accordingly, some embodiments provide for a method for generatingmagnetic resonance (MR) images of a subject from MR data obtained by amagnetic resonance imaging (MRI) system. The method comprises: (1)obtaining input MR spatial frequency data obtained by imaging thesubject using the MRI system; and (2) generating an MR image of thesubject from the input MR spatial frequency data using a neural networkmodel comprising: (a) a pre-reconstruction neural network (e.g.,pre-reconstruction neural network 210) configured to process the inputMR spatial frequency data; (b) a reconstruction neural network (e.g.,reconstruction neural network 212) configured to generate at least oneinitial image of the subject from output of the pre-reconstructionneural network; and (c) a post-reconstruction neural network (e.g.,post-reconstruction neural network 214) configured to generate the MRimage of the subject from the at least one initial image of the subject.

In some embodiments, the input MR spatial frequency data may beunder-sampled relative to a Nyquist criterion. For example, in someembodiments, the input MR spatial frequency data may include less than90% (or less than 80%, or less than 75%, or less than 70%, or less than65%, or less than 60%, or less than 55%, or less than 50%, or less than40%, or less than 35%, or any percentage between 25 and 100) of thenumber of data samples required by the Nyquist criterion. In someembodiments, the reconstruction neural network was trained toreconstruct MR images from spatial frequency MR data under-sampledrelative to a Nyquist criterion.

In some embodiments, the input MR spatial frequency data may have beenobtained using a non-Cartesian (e.g., radial, spiral, rosette, variabledensity, Lissajou, etc.) sampling trajectory, which may be used toaccelerate MRI acquisition and/or be robust to motion by the subject.

In some embodiments, the pre-reconstruction neural network comprises afirst neural network configured to suppress RF interference (e.g.,neural network 224), the first neural network comprising one or moreconvolutional layers. Additionally or alternatively, thepre-reconstruction neural network comprises a second neural networkconfigured to suppress noise (e.g., neural network 226), the secondneural network comprising one or more convolutional layers. Additionallyor alternatively, the pre-reconstruction neural network comprises athird neural network configured to perform line rejection (e.g., neuralnetwork 220), the third neural network comprising one or moreconvolutional layers.

In some embodiments, the reconstruction neural network is configured toperform data consistency processing using a non-uniform Fouriertransformation for transforming image data to spatial frequency data. Insome embodiments, the reconstruction neural network is configured toperform data consistency processing using the non-uniform Fouriertransformation at least in part by applying the non-uniform Fouriertransformation on data by applying a gridding interpolationtransformation, a fast Fourier transformation, and a de-apodizationtransformation to the data.

In some embodiments, the MRI system comprises a plurality of RF coils,the at least one initial image of the subject comprises a plurality ofimages, each of the plurality of images generated from a portion of theinput MR spatial frequency data collected by a respective RF coil in aplurality of RF coils, and the post-reconstruction neural networkcomprises a first neural network (e.g., neural network 232) configuredto estimate a plurality of RF coil profiles corresponding to theplurality of RF coils. In some such embodiments, the method furthercomprises: generating the MR image of the subject using the plurality ofMR images and the plurality of RF coil profiles.

In some embodiments, the at least one initial image of the subjectcomprises a first set of one or more MR images and a second set of oneor more MR images, and the post-reconstruction neural network comprisesa second neural network (e.g., neural network 234) for aligning thefirst set of MR images and the second set of MR images.

In some embodiments, the post-reconstruction neural network comprises aneural network (e.g., neural network 238) configured to suppress noisein the at least one initial image and/or at least one image obtainedfrom the at least one initial image.

In some embodiments, the pre-reconstruction neural network, thereconstruction neural network, and the post-reconstruction neuralnetwork are jointly trained with respect to a common loss function. Insome embodiments, the common loss function is a weighted combination ofa first loss function for the pre-reconstruction neural network, asecond loss function for the reconstruction neural network, and a thirdloss function for the post-reconstruction neural network.

The neural networks described herein may be configured to operate ondata in any suitable domain. For example, one or more of the neuralnetworks described herein may be configured to receive as input, data inthe “sensor domain”, “spatial-frequency domain” (also known as k-space),and/or the image domain. Data in the “sensor domain” may comprise rawsensor measurements obtained by an MRI system. Sensor domain data mayinclude measurements acquired line-by-line for a set of coordinatesspecified by a sampling pattern. A line of measurements may be termed a“readout” line. Each measurement may be a spatial frequency. As such,sensor domain data may include multiple readout lines. For example, if preadout lines were measured and each readout line included m samples,the sensor domain data may be organized in an m×p matrix. Knowing thek-space coordinates associated with each of the m×p samples, the sensordomain data may be re-organized into the corresponding k-space data, andmay be then considered to be spatial frequency domain data. Data in thesensor domain as well as the data in k-space is spatial frequency data,but the spatial frequency data is organized differently in these twodomains. Image-domain data may be obtained by applying an inverseFourier transformation (e.g., an inverse fast Fourier transform if thesamples fall on a grid) to k-space data.

In addition, it should be appreciated that the sensor domain, k-space,and image domain are not the only domains on which the neural networksdescribed herein may operate. For example, the data in a source domain(e.g., sensor domain, k-space, or image domain) may be furthertransformed by an invertible transformation (e.g., 1D, 2D, or # dFourier, Wavelet, and/or short-time Fourier transformation, etc.) to atarget domain, the neural network may be configured to receive as inputdata in the target domain, and after completing processing, the outputmay be transformed back to the source domain.

A neural network may be configured to operate on data in a particulardomain being trained to operate on input in the particular domain. Forexample, a neural network configured to operate on data in domain D, maybe trained on input-output pairs, with the input in the pairs being thedomain D. In some embodiments, the output of a neural network may be inthe same domain as its input, but in other embodiments, the input is notin the same domain as its input (e.g., the reconstruction neural network212 may receive input data in the spatial frequency domain and outputimages in the image domain).

As used herein, “high-field” refers generally to MRI systems presentlyin use in a clinical setting and, more particularly, to MRI systemsoperating with a main magnetic field (i.e., a B₀ field) at or above 1.5T, though clinical systems operating between 0.5 T and 1.5 T are oftenalso characterized as “high-field.” Field strengths betweenapproximately 0.2 T and 0.5 T have been characterized as “mid-field”and, as field strengths in the high-field regime have continued toincrease, field strengths in the range between 0.5 T and 1 T have alsobeen characterized as mid-field. By contrast, “low-field” refersgenerally to MRI systems operating with a B₀ field of less than or equalto approximately 0.2 T, though systems having a B₀ field of between 0.2T and approximately 0.3 T have sometimes been characterized as low-fieldas a consequence of increased field strengths at the high end of thehigh-field regime. Within the low-field regime, low-field MRI systemsoperating with a B₀ field of less than 0.1 T are referred to herein as“very low-field” and low-field MRI systems operating with a B₀ field ofless than 10 mT are referred to herein as “ultra-low field.”

In some embodiments, the techniques described herein for generating MRimages from input MR spatial frequency data may be adapted forapplication to spatial frequency data collected using a low-field MRIsystem, including, by way of example and not limitation, any of thelow-field MR systems described herein and/or any low-field MR systemsdescribed in U.S. Pat. No. 10,222,434, filed on Jan. 24, 2018, titled“Portable Magnetic Resonance Imaging Methods and Apparatus,” which isincorporated by reference in its entirety.

Following below are more detailed descriptions of various conceptsrelated to, and embodiments of, methods and apparatus for generating MRimages from spatial frequency domain data. It should be appreciated thatvarious aspects described herein may be implemented in any of numerousways. Examples of specific implementations are provided herein forillustrative purposes only. In addition, the various aspects describedin the embodiments below may be used alone or in any combination, andare not limited to the combinations explicitly described herein.

FIG. 2A is a diagram illustrating processing performed by a neuralnetwork model on data collected by an MRI system while imaging a subjectto generate an MR image of the subject, in accordance with someembodiments of the technology described herein. As shown in FIG. 2A,neural network model 204 may be configured to implement a deep learningpipeline to estimate one or more MR images 206 from input MR spatialfrequency data 202. The neural network model 204 may include multipleneural networks for performing various processing pipeline tasks. Insome embodiments, at least some (e.g., all) of the neural networks partof neural network model 204 may be trained jointly on a common set oftraining data and with respect to a common loss function.

It should be appreciated that although, in some embodiments, all tasksin the pipeline for generating MR images from input MR spatial frequencydata are performed by respective neural networks (e.g., part of neuralnetwork 204), in other embodiments, one or more such tasks may beperformed by techniques other than neural networks. Notwithstanding, insuch embodiments, the neural networks that are part of the processingpipeline may be trained jointly on a common set of training data andwith respect to a common loss function.

In the illustrated embodiment, neural network model 204 includespre-reconstruction neural network 210 configured to perform one or morepre-processing tasks (e.g., motion correction, RF interference removal,noise removal), reconstruction neural network 212 configured toreconstruct one or more images from the output of the neural network 210(e.g., including when the MR data is undersampled), andpost-reconstruction neural network 214 configured to perform one or morepost-processing tasks (e.g., combining images generated from datacollected by different coils, image registration, signal averaging,denoising, and correction for intensity variation) on the MR imagesgenerated by the reconstruction neural network 212. Aspects of thepre-reconstruction neural network 210 are described herein, includingwith reference to FIGS. 2B, and 4A-4D. Aspects of the reconstructionneural network 212 are described herein, including with reference toFIGS. 3A-3E. Aspects of the post-reconstruction neural network 214 aredescribed herein, including with reference to FIGS. 2C and 6-14. Aspectsof training neural network model 204 are described herein including withreference to FIG. 5.

In some embodiments, input MR spatial frequency data 202 may becollected by one or multiple RF coils of an MRI system. The data 202 maybe collected using a Cartesian sampling trajectory or any suitable typeof non-Cartesian sampling trajectory (e.g., radial, spiral, rosette,variable density, Lissajou, etc.). In some embodiments, the data 202 maybe fully-sampled data (data collected by sampling spatial frequencyspace so that the corresponding Nyquist criterion is not violated). Insome embodiments, the data 202 may be under-sampled data (datacontaining fewer points than what is required by spatial Nyquistcriteria). In some embodiments, the data 202 may exhibit artefacts dueto the presence of external RF interference, internal RF interference,and/or noise generated by the MR receiver chain and/or a subject (orobject) being imaged. In some embodiments, the data may includedistortions caused by movement of the patient during imaging.

FIG. 2B is a diagram of illustrative components of thepre-reconstruction neural network 210 part of the neural network model204 of FIG. 2A, in accordance with some embodiments of the technologydescribed herein. The pre-reconstruction neural network 210 may includeone, two, three, four, and/or any other suitable number of neuralnetworks each configured to perform a pre-processing task in the overalldata processing pipeline.

In the illustrated embodiment of FIG. 2B, pre-reconstruction neuralnetwork 210 includes three neural networks: (1) a neural network 220configured to perform line rejection; (2) a neural network 224configured to suppress RF interference (external and/or internal RFinterference); and (3) a neural network 226 configured to suppressnoise. In the illustrated embodiment, pre-reconstruction neural network210 includes all three neural networks 220, 224, and 226. In otherembodiments, neural network 210 may include any one or any two of theneural networks 220, 224, 226. Also, neural network 210 may include oneor more other neural networks for performing pre-processing tasks in thepipeline, as aspects of the technology described herein are not limitedin this respect.

In some embodiments, neural network 220 may be configured to processportions (e.g., readout lines) of sensor data 202 to determine whetherany of these portions are corrupted, for example, due to motion of thepatient during their acquisition. In some embodiments, the input toneural network 220 may be a portion (e.g., a readout line) of data 202,and the output of the neural network may provide an indication ofwhether or not the portion of data 202 is corrupted (e.g., due topatient motion).

In some embodiments, the input to neural network 220 may further includedata from one or more auxiliary sensors (e.g., one or more opticalsensors, one or more RF sensors, one or more accelerometers and/orgyroscopes) configured to detect patient movement. Such sensors may bepart of the MRI system that acquired the data 202 (e.g., one or more RFsensors, accelerometers, and/or gyroscopes may be coupled to a helmethousing one or more RF receive coils) or may be external to the MRIsystem but deployed so as to monitor patient movement (e.g., one or morecameras may be positioned to observe the imaging region and/or thepatient to detect patient movement).

In some embodiments, the neural network 220 may be a convolutionalneural network and may have one or more convolutional layers, one ormore transpose convolutional layers, one or more non-linearity layers,and/or one or more fully connected layers. The neural network 220 may beimplemented using any of the neural network architectures describedherein including with reference to FIG. 3D by way of example and notlimitation. Alternatively, a ResNet type architecture may be used whereconvolutional blocks have residual connections.

In some embodiments, the neural network 220 may be applied to the data202 after that data has been processed (e.g., by neural networks 224 and226) to suppress (e.g., reduce and/or eliminate) RF artefacts such as RFinterference and RF noise. In other embodiments, the neural network 220may be applied to the data 202 before it has been processed to suppressRF artefacts.

Returning to FIG. 2B, in some embodiments, neural network 224 may beconfigured to suppress RF interference. As described herein, RFinterference may be external RF interference generated by one or moredevices external to the MRI system, as the case may be for low-field MRIsystems deployed outside of shielded rooms (e.g., Faraday cages) invarious environments (e.g., emergency room, an ICU, an ambulance, adoctor's office, etc.) and in the presence of various devices (medicalequipment, smart phones, televisions, etc.). RF interference may alsoinclude internal RF interference generated by one or more components ofthe MRI system located outside of its imaging region (e.g., powersupply, gradient coils, gradient coil amplifiers, RF amplifiers, etc.).

In some embodiments, the neural network 224 may be a convolutionalneural network, and may have one or more convolutional layers, one ormore transpose convolutional layers, one or more non-linearity layers,one or more pooling layers (e.g., average, spectral, maximum) and one ormore corresponding unpooling layers, and/or one or more fully connectedlayers. The neural network 224 may be implemented using any of theneural network architectures described herein including with referenceto FIGS. 4A-4D by way of example and not limitation. Alternatively, aResNet type architecture may be used where convolutional blocks haveresidual connections.

In some embodiments, the neural network 224 may be trained usingparticular loss functions described next. First, some notation isintroduced. An MRI system may have one or multiple RF coils configuredto detect MR signals in the imaging region of the MR system. Let thenumber of such RF coils be denoted by N_(C). For each RF coil cconfigured to detect MR signals in the imaging region, let s_(c) denotethe detected signal. This detected signal contains three differentcomponents as follows: (1) the target MR signal data, x_(c) for coil c;(2) the noise n_(c) corrupting the signal (e.g., noise generated by theMR receiver chain for coil c, noise generated by the subject (or object)being imaged); and (3) external and/or internal RF interference i_(c).Accordingly, s_(c)=x_(c)+n_(c)+i_(c). Moreover, by locating N_(P) RFcoils outside of the system noise observed outside of the system (whichis correlated with s_(c)'s) called s_(c) ^(nz) may be acquired. Thus,the observed signal may expressed according to:

s _(c) =x _(c) +n _(c) +i _(c) =s _(c) ^(NI) +i _(c).

In some embodiments, the neural network 224 may be trained to suppressRF interference i_(c). To this end, training data may be created thatincludes all of the components of s_(c) separately so that ground truthis available. For example, each of x_(c), n_(c), and i_(c), may begenerated synthetically using a computer-based simulation and/or dataobserved using an MRI system. For example, to generate i_(c) one cansynthetically add structured noise lines to s_(c) or acquire s_(c) whileno object is located inside of the system. As another example, an MRIsystem may have one or more RF coils outside of the imaging region thatmay be used to observe artefacts outside of the imaging region (withoutalso detecting MR signals) and this coil or coils may be used to measureRF interference.

The input to the neural network 224 may be: (1) the signal s_(c) foreach coil, so that the neural network suppresses RF interference foreach coil separately; (2) the signals s_(c) for all the coils asseparate channels, so that the neural network suppresses RF interferencefor all coils at the same time; or (3) the signals s_(c) for each coil,as separate channels, as well as the signals s_(c) ^(nz)'s as extrainformation in other channels (not to be suppressed, but rather tosuppress RF interference in the signals s_(c). The output produced bythe neural network 224, corresponding to the input, may be: (1) s_(c)^(NI) for each coil c separately; or (2) all s_(c) ^(NI)'s as separatechannels (when the input is of the latter two cases). Additionally, insome embodiments, the input to this block can be s_(c) of all N_(avg)averages together to incorporate even more information. In this case theoutput will be all denoise coil data for all averages together. This maybe helpful when multiple observations are made by each coil.

Any of numerous types of loss functions may be used for training aneural network for suppressing RF interference, and various examples ofloss functions are provided herein. As one example, for training aneural network 224 for suppressing RF interference in data acquiredusing a single coil, the following loss function may be employed:

(θ)=∥F(s _(c) ^(NI))−f _(CNN)(F(s _(c))|θ)∥₂ ²

+∥f _(CNN)(∇F(s _(c))|θ)∥₁

+∥W(s _(c) ^(NI) −f _(CNN)(s _(c)|θ))∥

where W is the weighting matrix, F is a 1D Fourier (spectral) transform,∇ is an image gradient, and θ represents parameters of the neuralnetwork 224 denoted in the equations by f_(CNN).

In the multi-channel setting, the following loss function may beemployed for training neural network 224:

${\mathcal{L}(\theta)} = {\sum\limits_{c = 1}^{N_{coil}}\left( {{{{F\left( s_{c}^{NI} \right)} - {f_{CNN}\left( {F(s)} \middle| \theta \right)}_{c}}}_{2}^{2} + {{f_{CNN}\left( {\nabla{F(s)}} \middle| \theta \right)}_{c}}_{1} + {{W\left( {s_{c}^{NI} - {f_{CNN}\left( s \middle| \theta \right)}_{c}} \right)}}} \right)}$

where N_(coil) is the number of coils and f_(CNN)(s)_(c) is denoisedsensor data for coil c, where s includes all the signals s_(c) arrangedchannel-wise.

Returning to FIG. 2B, in some embodiments, neural network 226 may beconfigured to suppress noise. For example, neural network 226 may beconfigured to suppress noise generated by operation of circuitryinvolved in the processing of signals recorded by the RF coil(s) of theMRI system, which circuitry may be termed the “MR receiver chain”. TheMR receiver chain may include various types of circuitry such as analogcircuitry (e.g., one or more amplifiers, a decoupling circuit, an RFtransmit/receive switch circuit, etc.), digital circuitry (e.g., aprocessor) and/or any suitable combination thereof. Some examples of MRreceiver chain circuitry are described in U.S. Pat. App. Pub. No.:2019/0353723, filed on May 21, 2019 (as application Ser. No.16/418,414), titled “Radio-Frequency Coil Signal Chain For a Low-FieldMRI System”, which is incorporated by reference in its entirety.

In some embodiments, the neural network 226 may be a convolutionalneural network, and may have one or more convolutional layers, one ormore transpose convolutional layers, one or more non-linearity layers,one or more pooling layers (e.g., average, spectral, maximum) and one ormore corresponding unpooling layers, and/or one or more fully connectedlayers. The neural network 226 may be implemented using any of theneural network architectures described herein including with referenceto FIGS. 4A-4D by way of example and not limitation. Alternatively, aResNet type architecture may be used where convolutional blocks haveresidual connections.

In some embodiments, the input to the neural network 226 may be: (1)s_(c) for suppressing noise from each coil c separately; (2) all s_(c)'sas separate channels, for suppressing noise in all coils at the sametime; (3) all s_(c)'s as separate channels as well as the data detectedby coils outside of the imaging region (s_(p) ^(nz)) as an additionalinformation to use for denoising. In some embodiments, the output of thetrained neural network may be: (1) x_(c) or (2) all x_(c)'s for themultiple coils.

Any of numerous types of loss functions may be used for training theneural network 226 for suppressing noise. For example, for training aneural network for suppressing noise in data acquired using a singlecoil, the following loss function may be employed:

(θ)=∥F(x)−f _(CNN)(F(s _(c))|θ)∥₂ ²

+∥f _(CNN)(∇F(s _(c))|θ)∥₁

+∥W(x _(c) −f _(CNN)(s _(c)|θ))∥

In some embodiments, when training neural network 2266 for suppressingnoise in data acquired using multiple coils, the following loss functionmay be employed:

${\mathcal{L}(\theta)} = {\sum\limits_{c = 1}^{N_{coil}}{\left( {{{{F\left( x_{c} \right)} - {f_{CNN}\left( {F(s)} \middle| \theta \right)}_{c}}}_{2}^{2} + {{f_{CNN}\left( {\nabla{F(s)}} \middle| \theta \right)}}_{1} + {{W\left( {x_{c} - {f_{CNN}\left( s \middle| \theta \right)}_{c}} \right)}}} \right).}}$

FIG. 2C is a diagram of illustrative components of thepost-reconstruction neural network 214 part of the neural network model204 of FIG. 2A, in accordance with some embodiments of the technologydescribed herein. As shown in FIG. 2C, reconstruction neural network 212may generate one or multiple MR images upon reconstruction—these are theinitial MR images 230-1, 230-2, . . . , 230-N.

There are multiple reasons for why reconstruction neural network 212 maygenerate multiple MR images. For example, in some embodiments, an MRIsystem may include multiple RF coils and the reconstruction neuralnetwork 212 may generate, for each particular one of the multiple RFcoils, one or more MR images from data detected by that particular RFcoil. Moreover, multiple images may be generated by the neural network212 even from data collected by a single RF coil because: (1) each linemay be acquired multiple times (for subsequent averaging to boost SNR);and (2) the data collected by a single RF coil may include datacorresponding to each of multiple two-dimensional slices of a patient'sanatomy. Accordingly, in some embodiments, the initial images 230-1, . .. , 230-N, may include multiple sets of MR images, with each of the setsof MR images generated using data collected by a respective RF coil fromamong the multiple RF coils of the MRI system, and each set of imagesmay include one or multiple volumes of data (e.g., K volumes of dataeach including M slices per volume). However, in some embodiments, thecollected MR data may be such that the reconstruction neural network 212may generate only a single MR image, as aspects of the technologydescribed herein are not limited in this respect.

In the illustrated embodiment of FIG. 2C, post-reconstruction neuralnetwork 214 includes five neural networks: (1) a neural network 232configured to perform RF coil profile estimation and/or imagecombination across RF coils; (2) a neural network 234 configured performalignment among multiple sets of one or more MR images to correct forpatient motion; (3) a neural network 236 configured to perform signalaveraging; (4) a neural network 238 configured to perform noisesuppression; and (5) a neural network 240 configured to performintensity correction.

In the illustrated embodiment of FIG. 2C, post-reconstruction neuralnetwork 214 includes all five neural networks 232, 234, 236, 238, and240. In other embodiments, neural network 214 may include any one, orany two, or any three, or any four of the neural networks 232, 234, 236,238, and 240. Also, neural network 214 may include one or more otherneural networks for performing post-processing tasks in the pipeline, asaspects of the technology described herein are not limited in thisrespect.

Neural network 232 may be used in embodiments in which the MRI systemcollects data using multiple RF coils. In such embodiments, the neuralnetwork 232 may be used to combine the images (from among initial images232) generated from data collected by different RF coils, butcorresponding to the same slices. As described in more detail below inthe “Coil Estimation” Section below, neural network 232 may be used toeither estimate such a combined image directly or to estimatesensitivity profiles for the different RF coils, which in turn may beused to combine the images.

In some embodiments, the neural network 232 may be a convolutionalneural network having one or more convolutional layers, one or moretranspose convolutional layers, one or more non-linearity layers, one ormore pooling layers and one or more corresponding unpooling layers,and/or one or more fully connected layers. For example, in someembodiments, the neural network 232 may have the architecture shown inFIG. 20B. Alternatively, a ResNet type architecture may be used whereconvolutional blocks have residual connections.

Returning to FIG. 2C, in some embodiments, neural network 234 may beconfigured to align two sets of one or more MR images to each other. Insome instances, each set of MR images may correspond to a set of imagesfor a given volume (e.g., a number of 2D slices that may be stacked toconstitute a volume). Such an alignment allows for the sets of MR imagesto be averaged to increase the SNR. Performing the averaging withoutfirst performing alignment would introduce blurring due to, for example,movement of the patient during acquisition of the data being averaged.

In some embodiments, neural network 234 may be configured to align setsof one or more MR images by estimating one or more transformations(e.g., non-rigid, affine, rigid) between the sets of MR images. In someembodiments, neural network 234 may be implemented at least in part byusing estimated parameter resampling (EPR). Aspects of illustrativeimplementations the neural network 234 are described herein including inthe “Motion Correction” Section below.

Returning to FIG. 2C, in some embodiments, neural network 236 may beconfigured to perform signal averaging to increase the SNR of the finalreconstructed MR image. Conventionally, this is performed by averagingmultiply acquired data from the same imaging protocol (e.g., the samepulse sequence being repeatedly applied). An assumption underlying thisconventional approach is that the images being averaged have almostindependent and identically distributed (iid) noise, which will cancelwhen the images are combined. In practice, however, this assumption maybe violated because the reconstruction is non-linear and because biasand correlation may be introduced by the MRI system.

The inventors have recognized that improved performance may be achievedif, instead of averaging images, a neural network is used to learn howto combine them. This would take into account various characteristics ofthe noise and MRI system that result in the iid assumption beneath theconventional averaging approach being violated. Suppose x is the groundtruth target to be reconstructed. Suppose also that N_(avg) measurementsof x are acquired and individually reconstructed, yielding images x₁, .. . , x_(N) _(avg) . Instead of averaging these images, the combinationmay be performed by neural network 236 denoted by f_(cnn)(.|θ), whichtakes all N_(avg) images as input and outputs a single combined imagex_(rec).

In some embodiments, the neural network 236 may be applied after neuralnetwork 234 is used to align corresponding sets of images so thatblurring is not introduced through the combination performed by neuralnetwork 236.

The neural network 236 may be a convolutional neural network having oneor more convolutional layers, one or more transpose convolutionallayers, one or more non-linearity layers, one or more pooling layers andone or more corresponding unpooling layers, and/or one or more fullyconnected layers. For example, the network 236 may have a U-net typearchitecture. Alternatively, a ResNet type architecture may be usedwhere convolutional blocks have residual connections.

In some embodiments, given the dataset

, the neural network may be trained using the following loss function:

${\mathcal{L}(\theta)} = {\sum\limits_{j = 1}^{||}{{x^{(j)} - x_{rec}^{(j)}}}_{2}}$

Returning to FIG. 2C, in some embodiments, neural network 238 may beconfigured to suppress artefacts in the image domain. The neural network238 may be a convolutional neural network, and may have one or moreconvolutional layers, one or more transpose convolutional layers, one ormore non-linearity layers, one or more pooling layers (e.g., average,spectral, maximum) and one or more corresponding unpooling layers,and/or one or more fully connected layers. The neural network 238 may beimplemented using any of the neural network architectures describedherein including with reference to FIGS. 4A-4D by way of example and notlimitation. Alternatively, a ResNet type architecture may be used whereconvolutional blocks have residual connections.

Suppressing artefacts in the image domain may facilitate reducing orremoving noise generated by the acquisition system (e.g., MR receiverchain). The effects of such noise are more pronounced in low-field MRIsystem leading to a lower signal to noise ratio. Conventional techniquesfor suppressing noise in MR images involve using parametric filteringtechniques such as anisotropic diffusion or non-local means filtering.The goal of these parametric filtering techniques is to remove noise inuniform image regions while preserving sharpness of the edges aroundanatomical structures. When the level of noise is high (as the case maybe in low-field systems), applying the parametric filters typicallyresults in smooth-looking images with loss of detail in low-contrastimage regions. By contrast, using deep learning to suppress artefacts(e.g., noise) in the image domain using the neural network 238 resultsin sharp-looking images, while preserving structure even in low-contrastregions.

In some embodiments, training data may be created to reflect the effectof noise on MR images. The noise may be measured (e.g., using an MRIsystem) or synthesized. For example, a synthetic noise signal e_(c) maybe added to the image x_(c) as follows: x_(c) ^(n)=x_(c)+e_(c), wherethe noise may be drawing from a Gaussian e_(c)˜N(0, σ_(c)) or Riciandistribution, (assuming there is no correlation among coils forsimplicity). In some embodiments, the neural network 238 may be trained,given a dataset

, using content loss (structural similarity index (SSIM) loss or meansquared error loss) and an adversarial loss given by:

${\mathcal{L}\left( {\theta_{G},\ \theta_{D}} \right)} = {{\sum\limits_{i = 1}^{||}{- {D_{\theta_{D}}\left( {{G_{\theta_{G}}\left( x_{c} \right)},\ x_{c}^{n}} \right)}}} + {{\lambda \left( {1 - {{SSIM}\ \left( {x_{c}x_{c}^{n}} \right)}} \right)}.}}$

In the above expression for loss, the generator G is the filteringnetwork and the discriminator D is trained to best differentiate betweenimages filtered with the network G and original noise-free images(ground truth). In some embodiments, the parameters of the generator(θ_(G)) and discriminator (θ_(D)) neural networks may be optimized byestablishing a minimax game between the generator and discriminatorneural networks. The generator network may be trained to producefiltered images as close as possible to the ground truth and thus foolthe discriminator neural network. On the other hand, the discriminatornetwork may be trained to classify the input images as filtered orground truth. Using an adversarial loss, like the one described above,helps to achieve sharp-looking filtered images while preservingstructures even in low-contrast regions.

Returning to FIG. 2C, in some embodiments, neural network 240 mayconfigured to suppress (e.g., reduce and/or eliminate) inhomogeneousintensity variations across image regions, which may result fromcombining images generated from data collected by different RF coils(e.g., via the application of neural network 232).

In some embodiments, the neural network 240 may be a convolutionalneural network, and may have one or more convolutional layers, one ormore transpose convolutional layers, one or more non-linearity layers,one or more pooling layers (e.g., average, spectral, maximum) and one ormore corresponding unpooling layers, and/or one or more fully connectedlayers. The neural network 240 may be implemented using a U-Netarchitecture. Alternatively, a ResNet type architecture may be usedwhere convolutional blocks have residual connections.

To generate training data for training neural network 240, imageaugmentation may be employed to simulate the intensity variations usingunperturbed input images and a random histogram augmentation functionI_((x)):

x″=I(x′)

In some embodiments, the histogram augmentation function may be designedto enhance image contrast. Other image acquisition artifacts can bemodeled this way as well. For example, geometric transformations appliedto images, such as affine or nonlinear deformations T(r) yielding:

x″=I(x′(T(r))).

FIG. 2D is a flowchart of an illustrative process 250 for generating anMR image from input MR spatial frequency data, in accordance with someembodiments of the technology described herein. Process 250 may beperformed by any suitable computing device(s). For example, process 250may be performed by one or more processors (e.g., central processingunits and/or graphics processing units) part of the MRI system and/or byone or more processors external to the MRI system (e.g., computers in anadjoining room, computers elsewhere in a medical facility, and/or on thecloud).

Process 250 begins at act 252, where the system performing process 250obtains (e.g., accesses from memory or other non-transitory computerreadable storage medium, receives over a network) input MR spatialfrequency data obtained by imaging a subject using an MRI system. In theillustrative embodiment of FIG. 2D, the imaging itself is not part ofprocess 250. However, in other embodiments, process 250 may includeperforming the imaging using the MRI system.

The input MR spatial frequency data may include data collected by one ormultiple RF coils of the MRI system. The data 252 may be collected usinga Cartesian sampling trajectory or any suitable type of non-Cartesiansampling trajectory (e.g., radial, spiral, rosette, variable density,Lissajou, etc.). In some embodiments, the data 252 may be fully-sampleddata (data collected by sampling spatial frequency space so that thecorresponding Nyquist criterion is not violated). In some embodiments,the data 252 may be under-sampled data (data containing fewer pointsthan what is required by spatial Nyquist criteria). In some embodiments,the data 252 may be data corresponding to a slice or multiple slices,and may include multiple acquisitions of the same slice or volume sothat these acquisitions may be subsequently averaged.

Next, process 250 proceeds to act 254, where one or more MR images aregenerated from the input MR spatial frequency data. The MR image(s) maybe generated using a neural network model (e.g., neural network model204, described herein with reference to FIG. 2A). In some embodiments,the neural network model may include: a pre-reconstruction neuralnetwork (e.g., neural network 210), a reconstruction neural network(212), and a post-reconstruction neural network (214). Examplearchitectures and other aspects of such networks are described herein.

Accordingly, in some embodiments, generating MR image(s) from input MRspatial frequency data at act 254 comprises: (1) processing, at 256,input MR spatial frequency data using a pre-reconstruction neuralnetwork (e.g., neural network 210); (2) generating, at 258 and based onoutput of the pre-reconstruction neural network, at least one initialimage of the subject using a reconstruction neural network (e.g. neuralnetwork 212); and (3) generating, at 260, at least one MR image of thesubject from the at least one initial image of the subject obtainedusing the reconstruction neural network. The image(s) generated at act260 may then be saved, sent to another system, displayed, or output inany other suitable way.

It should be appreciated that any of the convolutional neural networkmodels described herein may be two-dimensional or three-dimensionalconvolutional neural networks that operate on two-dimensional data(e.g., data corresponding to a single image, for example, an image of aslice of a patient's anatomy) or three-dimensional data (e.g., datacorresponding to multiple images, for example, a stack of images in avolume each of which corresponds to a respective slice of the patient'sanatomy), as aspects of the technology described herein are not limitedin this respect.

Example Neural Network Architectures for Generating MR Images fromUndersampled Data

As described herein, the inventors have developed neural network modelsfor reconstructing MR images from spatial frequency data obtained usingnon-Cartesian sampling trajectories. For example, as described withreference to FIG. 2A, the reconstruction may be performed byreconstruction neural network 212, in some embodiments. Reconstructionneural network 212 may be implemented in any suitable way including inany of the ways described next with reference to FIGS. 3A-3E and/or inany of the ways described in U.S. Pat. Pub. No.: 2020/0034998, filedJul. 29, 2019 (as U.S. application Ser. No. 16/524,598), titled “DeepLearning Techniques for Magnetic Resonance Image Reconstruction”, whichis incorporated by reference in its entirety.

FIG. 3A is a diagram of an illustrative architecture of an exampleneural network model 310, which generates MR images from input MRspatial frequency data in stages. Input MR spatial frequency data 305 isfirst processed using initial processing block 312 to produce an initialimage 314, and then the initial image 314 is processed by a series ofneural network blocks 316-1, 316-2, . . . , 316-n.

In some embodiments, one or more of the blocks 316-1, 316-2, . . . ,316-n may operate in the image domain. In some embodiments, one or moreof the blocks 316-1, 316-2, . . . , 316-n may transform the input datato a different domain, including but not limited to the spatialfrequency domain, perform processing in the different domain, andsubsequently transform back to the image domain.

In some embodiments, the initializer block transforms the input MRspatial frequency data to the image domain to generate an initial imagefor subsequent processing by the neural network model 310. Theinitializer block may be implemented in any suitable way, and in someembodiments, the initializer block may employ a Fourier transformation,a non-uniform Fourier transformation, or a gridding reconstruction toobtain the initial image.

In some embodiments, one or more of the blocks 316-1, 316-2, . . . ,316-n may have the architecture of illustrative block 316-i in FIG. 3B,which includes a data consistency block 320, and a convolutional neuralnetwork block 350, both of which are applied to the input x_(i), labeled321. The input x_(i) may represent the MR image reconstruction generatedby neural network 310 at the completion of the (i−1)^(st) neural networkblock. The output 335 of the block 316-i is obtained by applying thedata consistency block 320 to the input x_(i), to obtain a first result,applying the convolutional neural network block 350 to x_(i), to obtaina second result, and subtracting from x_(i) a linear combination of thefirst result and the second result, where the linear combination iscalculated using the block-specific weight λ_(i).

In some embodiments, the data consistency block 320 may perform dataconsistency processing by transforming the input image represented byx_(i) to the spatial frequency domain using a non-uniform Fouriertransformation, comparing the result with the initial MR spatialfrequency data 305, and transforming the difference between the two backto the image domain using an adjoint of the non-uniform Fouriertransformation.

FIG. 3C shows an example implementation of data consistency block 320,in which the image domain input 322, is transformed to the spatialfrequency domain through a series of transformations 324, 326, and 328,whose composition is used to implement a non-uniform fast Fouriertransformation from the image domain to the spatial frequency domain.The transformation 324 is a de-apodization and zero-paddingtransformation D, the transformation 326 is an oversampled FFTtransformation F_(s), and the transformation 328 is the griddinginterpolation transformation G. The non-uniform fast Fouriertransformation A is represented by the composition of thesetransformations according to: A=G Fs D. Example realizations of theseconstituent transformations are described herein.

After the image domain input 322 is transformed to the spatial frequencydomain, it is compared with the initial MR spatial frequency data 305,and the difference between the two is transformed back to the imagedomain using the transformations 330, 332, and 334, in that order. Thetransformation 330 is the adjoint of the gridding interpolationtransformation 328. The transformation 332 is the adjoint of theoversampled FFT transformation 326. The transformation 334 is theadjoint of the de-apodization transformation 324. In this way, thecomposition of the transformations 330, 332, 334, which may be writtenas D^(H)F^(H) _(s)G^(H)=A^(H), represents the adjoint A^(H) of thenon-uniform Fourier transformation A.

In some embodiments, the convolutional neural network block 350 may havemultiple convolutional layers. For example, as shown in FIG. 3D, theblock 350 may have a U-net structure, whereby multiple convolutionallayers downsample the data and subsequent transpose convolutional layersupsample the data. In the example of FIG. 3D, input to the convolutionalnetwork block 350 is processed by a downsampling path followed anupsampling path. In the downsampling path, the input is processed byrepeated application of two convolutions with 3×3 kernels, each followedby application of a non-linearity (e.g., a ReLU), an average 2×2 poolingoperation with stride 2 for downsampling. At each downsampling step thenumber of feature channels is doubled from 64 to 128 to 256. In theupsampling path, the data is processed be repeated upsampling of thefeature map using an average unpooling step that halves the number offeature channels, a concatenation with the corresponding feature mapfrom the downsampling path, and two 3×3 convolutions, each followed byapplication of a non-linearity.

FIG. 3E is a diagram of another type of architecture of a block that maybe used within the neural network model of FIG. 3A. A neural networkmodel with blocks having the architecture like the one shown in FIG. 3Emay be termed a “generalized non-uniform variational network” or “GNVN”.It is “generalized” in the sense that, while data consistency blocks arenot used directly, features similar to the image features generated bysuch blocks may be useful to incorporate into a neural network model.

As shown in FIG. 3E, the i^(th) GNVN block 360-i takes as input: (1) theimage domain data x_(i), labeled as 362; and (2) the initial MR spatialfrequency data 364. The input x_(i) may represent the MR imagereconstruction generated by neural network 310 at the completion of the(i−1)^(st) GNVN block (360-(i−1)). These inputs to the block 360-i areused to generate input to the convolutional neural network (CNN) block372 part of block 360-i. In turn, the CNN block 372 generates the nextMR image reconstruction denoted by x_(i+1).

In the embodiment of FIG. 3E, the inputs 362 and 364 are used togenerate three inputs to the CNN block 372: (1) the reconstruction x_(i)itself is provided as input to the CNN block; (2) the result ofapplying, to the reconstruction x_(i), the non-uniform Fouriertransformation 366 followed by a spatial frequency domain CNN 368,followed by the adjoint non-uniform Fourier transformation 370; and (3)the result of applying, to the initial MR spatial frequency data 364,the spatial frequency domain convolutional neural network 368 followedby an adjoint non-uniform Fourier transform 370. The non-uniform Fouriertransformation 366 may be the transformation A expressed as acomposition of three transformations: the de-apodization transformationD, an oversampled Fourier transformation F_(s), and a local griddinginterpolation transformation G such that A=G F_(s) D. The spatialfrequency domain CNN 368 may be a five-layer convolutional neuralnetwork with residual connections. In other embodiments, the network 368may be any other type of neural network (e.g., a fully convolutionalnetwork, a recurrent network, and/or any other suitable type of neuralnetwork), as aspects of the technology described herein are not limitedin this respect.

A discussion of further aspects and details of neural network models forMR image reconstruction from non-Cartesian data, such as the neuralnetwork models illustrated in FIGS. 3A-3E, follows next. Let x∈

^(N) denote a complex-valued MR image to be reconstructed, representedas a vector with N=N_(x)N_(y) where N_(x) and N_(y) are width and heightof the image. Let y∈

^(M)(M<<N) represent the undersampled k-space measurements from whichthe complex-valued MR image x is to be reconstructed. Reconstructing xfrom y may be formulated as an unconstrained optimization problemaccording to:

$\begin{matrix}{{{\underset{x}{\arg \; \min}\frac{\lambda}{2}{{{Ax} - y}}_{2}^{2}} + {(x)}},} & \left( {{Eq}.\mspace{14mu} 1} \right)\end{matrix}$

where the operator A is a non-uniform Fourier sampling operator,

expresses regularisation terms on x, and λ is a hyper-parameterassociated to the noise level. When the k-space measurements y areobtained using a Cartesian sampling trajectory, the operator A mayexpressed according to: A=MF where M is a sampling mask, and F isdiscrete Fourier transform. In the case of a non-Cartesian samplingtrajectory, the measurements no longer fall on a uniform k-space gridand the sampling operator A is now given by a non-uniform discreteFourier transform of type I:

$\begin{matrix}{{y\left( \left( {k_{x},k_{y}} \right) \right)} = {\sum\limits_{l = 0}^{N_{x}}{\sum\limits_{m = 0}^{N_{y}}{x_{lm}{e^{2\; \pi \; i}\left( {{\frac{l}{N_{x}}k_{x}} + {\frac{m}{N_{y}}k_{y}}} \right)}}}}} & \left( {{Eq}.\mspace{14mu} 2} \right)\end{matrix}$

where (k_(x), k_(y))∈

² (rather than (k_(x), k_(y))∈

²). An efficient implementation of the above forward model may beimplemented using the so-called non-uniform Fast Fourier Transform(NUFFT), whereby Eq. 2 is approximated by the decomposition: A=GF_(s)D,where G is a gridding interpolation kernel, F_(s) is fast Fouriertransform (FFT) with an oversampling factor of s, and D represents ade-apodization weights.

Inversion of A is more involved. For the (approximately) fully-sampledcase, one can consider direct inversion (

(N³)) or a more computationally efficient gridding reconstruction, whichhas the form x_(gridding)=A^(H)Wy, where W is a diagonal matrix used forthe density compensation of non-uniformly spaced measurements. For theundersampled case, the inversion is ill-posed, and Eq. 1 should besolved by iterative algorithms.

The inventors have developed a new deep learning algorithm toapproximate the solution to the optimization problem of Eq. 1. Theapproach begins by considering a gradient descent algorithm, whichprovides a locally optimal solution to Eq. 1, specified by the followingequations for initialization and subsequent iterations:

x ₀ =f _(init)(A,y);  (Eq. 3)

x _(i+1) =x _(i)−α_(i)∇_(x) f(x)_(x=x) _(i) ,  (Eq. 4)

where f_(init) is an initializer, α is a step size and ∇f is thegradient of the objective functional, which is given by:

∇_(x) f(x)=λA ^(H)(Ax−y)+∇_(x)

(x).  (Eq. 5)

In some embodiments, the initializer may be the adjoint f_(init)(A,y)=A^(H)y reconstruction or the gridding reconstruction f_(init)(A,y)=A^(H)Wy. The deep learning approach to solving Eq. 1 involvesunrolling the sequential updates of Eq. 4 into a feed-forward model, andapproximating the gradient term ∇

by a series of trainable convolutional (or other types of neuralnetwork) layers and non-linearities. This approach results in anend-to-end trainable network with N_(it) blocks given by:

$\begin{matrix}{x_{0} = {f_{{init} - {cnn}}\left( {A,\left. y \middle| \theta_{0} \right.} \right)}} & \left( {{Eq}.\mspace{14mu} 6} \right) \\{x_{i + 1} = {x_{i} - {\lambda_{i}\; \underset{\underset{{DC} - i}{}}{A^{H}\left( {{Ax}_{i} - y} \right)}} - \underset{\underset{{CNN} - i}{}}{f_{cnn}\left( x_{i} \middle| \theta_{i} \right)}}} & \left( {{Eq}.\mspace{14mu} 7} \right)\end{matrix}$

where the learnable parameters are {θ₀, . . . , θ_(N) _(it) , λ₁, . . ., λ_(N) _(it) }. The step size α_(i) may be absorbed in the learnableparameters. In this way, a general non-convex regularization functionalis used, which may be approximated by convolutional neural networks. Forexample, the neural network models of FIGS. 3A-3D may implemented basedon Equations 6 and 7. For example, the data consistency term DC-i in Eq.6 may be implemented as shown in FIG. 3C, and the CNN-i term in Eq. 6may be implemented is shown in FIG. 3D.

Further details of the decomposition of the forward operator A=GF_(s)Dare described next. The spatial frequency domain may be indexed usingtwo-dimensional or three-dimensional coordinates (e.g. (k_(x), k_(y)) or(k_(x), k_(y), k_(z))). Each entry of the vector y representing input MRspatial frequency data represents a value associated to a specifick-space coordinate. A regular grid in k-space refers to aregularly-spaced grid of points k-space such that there is a fixeddistance Δ between each k-space coordinate that can be indexed.Generally, the input MR spatial frequency data y may include k-spacesamples spaced on a regular-grid or irregularly spaced. Regularly spacedpoints are sometimes termed Cartesian data points. Irregularly spacedpoints are sometimes termed non-Cartesian (data) points.

The interpolation transformation G operates to interpolate non-Cartesiansensor data y onto a regular k-space grid. When the transformation isrepresented as a matrix G, each row in the matrix corresponds to aspecific regular grid point in k-space, and the entry j in the row i(i.e., the entry G_(ij)) expresses how much weight is associated betweenith regular grid and jth k-space sample. In some embodiments, theinterpolation matrix entries may be computed using any one of thefollowing four functions:

${{Two}\mspace{14mu} {term}\mspace{14mu} {cosine}\mspace{14mu} \alpha} + {\left( {1 - \alpha} \right){\cos \left( {\frac{2\; \pi}{W}u} \right)}}$${{Three}\text{-}{term}\mspace{14mu} {cosine}\text{:}\mspace{14mu} \alpha} + {\beta \; {\cos \left( {\frac{2\pi}{W}u} \right)}} + {\left( {1 - \alpha - \beta} \right){\cos \left( {\frac{4\; \pi}{W}u} \right)}}$${Gaussian}\text{:}\mspace{14mu} {\exp \left\lbrack {{- \frac{1}{2}}\left( \frac{u}{\sigma} \right)^{2}} \right\rbrack}$${Kaiser}\text{-}{Bessel}\text{:}\mspace{14mu} \frac{1}{W}{I_{0}\left\lbrack {\beta \mspace{11mu} \sqrt{1 - \left( {2\; {u/W}} \right)^{2}}} \right\rbrack}$

where u is a distance between ith regular grid point and jthnon-Cartesian data coordinate. The parameters α, β, W, σ are free designparameters to be specified by user, and I₀ is the zeroth-order modifiedBessel function of the first kind. Other functions may be used tocompute interpolation matrix entries instead of or in addition to theabove example functions.

In some embodiments, the Fourier transformation F may be represented byan oversampled Fourier matrix F_(s), which is a dense matrix in whicheach entry is a complex exponential of the form e^(iγ) for γ whichdepends on the index. The role of this matrix is to perform Fouriertransform. In some embodiments, F_(s) may be implemented using the fastFourier transform with oversampling factor s. For example, if the imageto be reconstructed x is N×N pixels, then oversampling FFT is performedfor image size sN×sN.

In some embodiments, the de-apodization transformation may berepresented by a matrix D that will weigh each pixel in the image by acorresponding weight to reduce the interpolation error of approximatingA with the given decomposition. In some embodiments, this may beimplemented via a pixel-wise weighting of the intermediatereconstruction in the image domain. For example, the pixel-wiseweighting may be implemented using a spatially-varying low-order smoothpolynomial. In some embodiments, the matrix D may be set as described inSection IV-C of Fessler, J. A., Sutton B. P.: Non-uniform fast Fouriertransforms using min-max interpolation. IEEE Transactions of SignalProcessing 51(2), 560-574 (2003), which is incorporated by reference inits entirety.

The neural network architectures described herein with reference toFIGS. 3A-3D, may be considered as embodiments of a more general neuralnetwork model that may be expressed according to the following:

x _(rec) =f _(rec)(A,y|θ)  (Eq. 8),

which accepts as input any input that is a combination of the forwardoperator A and raw spatial frequency data y. The learnable parameters θmay be adjusted during training process.

The input to the neural network of Eq. 8 may be data obtained by one ormultiple RF coils of an MRI system. The input data y may have beenobtained using multiple contrasts and/or different sets of acquisitionparameters (e.g., by varying repetition time (TR), echo time (TE), flipangle θ, etc.). In some embodiments, input into the network may be, butis not limited to, the raw data y. Additionally or alternatively, theinput to the network may be the adjoint reconstruction A^(H)y where(.)^(H) is the conjugate transpose of the matrix.

In some embodiments, where the data y includes data collected bymultiple RF coils, these data y may be split into N_(coil) separate datasets, denoted y^((i)) for i=1, . . . , N_(coil). In some suchembodiments, the neural network input may be the adjoint reconstructionof each coil images x₀ ^((i))=A^(H)y^((i)), and x₀ ^((i)) for i=1, . . ., N_(coil) can be stacked together and form the input to the network(e.g., to the convolutional layers part of the network).

In some embodiments, the raw data y may include multiple measurementsobtained by each of one or more RF coils. For example, if the data ismeasured multiple times, say N_(avg) times, then these data, or theadjoint reconstruction of these data, or any other function of thesedata measurements and the forward operator A, may form an input to theneural network. For example, multiple measurements may be obtained forsignal averaging and/or as part of acquiring images with differentcontrast.

It should also be appreciated that the neural network of Eq. 8 need notoperate on the raw data y, and in some embodiments these data may bepre-processed. For example, in some embodiments these data may bepre-processed to perform operations such as interference removal,denoising, filtering, smoothing, image prewhitening, etc. The outputx_(rec) of the neural network in Eq. 8, the output may include one ormore images per respective RF coil. For example, if the input datacontains data from each of N_(coil) RF coils, the output may include oneMR image for each such RF coil or multiple MR images for each such coil(e.g., when each coil performs multiple acquisitions, for example, usingdifferent contrasts).

Example Neural Network Architectures for Pre-Reconstruction ArtefactSuppression

As described above with reference to FIG. 2B, pre-reconstruction neuralnetwork 210 may be configured to suppress various types of artefacts inthe MR spatial frequency data. The suppression may involve rejectinglines of collected data (e.g., using neural network 220), suppressing RFinterference (e.g., using neural network 224), and/or suppressing noise(e.g., using neural network 226). The neural networks 224 and/or 226 maybe implemented in any suitable way including in any of the waysdescribed next with reference to FIGS. 4A-4D and/or in any of the waysdescribed in U.S. Pat. Pub. No.: 2020/0058106, filed Aug. 15, 2019 (asU.S. application Ser. No. 16/541,511), titled “Deep Learning Techniquesfor Suppressing Artefacts in Magnetic Resonance Images,” which isincorporated by reference in its entirety. As yet another example, theneural networks 224 and/or 26 may be implemented using one or more otherarchitectures such as, for example, a ResNet architecture comprisingconvolutional blocks with residual connections, as described in He K,Zhang X, Ren S, Sun J. “Deep residual learning for image recognition.”In Proceedings of the IEEE conference on computer vision and patternrecognition 2016 (pp. 770-778), which is incorporated by reference inits entirety.

In some embodiments, the neural network 224 for suppressing RFinterference may be implemented as a neural network having a “U”structure with convolutional layers being first applied to a sequence ofsuccessively lower-resolution versions of the data (along thedown-sampling path) and, second, to a sequence of successivelyhigher-resolution versions of the data (along the up-sampling path). Anexample of such an architecture is shown in FIG. 4A as architecture 430.

As shown in FIG. 4A, in the down-sampling path, convolutional layers 432a and 432 b are applied to input 431. An average pooling layer 433 isthen applied to the output of convolutional layer 432 b, andconvolutional layers 434 a and 434 b are applied to the lower-resolutiondata produced by the average pooling layer 433. Next, another averagepooling layer 435 is applied to the output of convolutional layer 434 b,and convolutional layers 436 a, 436 b, and 436 c are applied to theoutput of the average pooling layer 435.

Next, in the up-sampling path, the output of convolutional layer 436 cis processed by the average unpooling layer 437. The output of theaverage unpooling layer 437 is processed by convolutional layers 438 aand 438 b. The output of convolutional layer 438 b is processed byaverage unpooling layer 439, and the output of average unpooling layer439 is processed by convolutional layers 440 a-c to generate output 445.

The architecture 430 also includes skip connections 441 and 442, whichindicates that the input to the average unpooling layers consists fromoutput by the immediately preceding convolutional layer and outputhaving a higher resolution generated by another (not immediately)preceding convolutional layer. For example, the input to the averageunpooling layer 437 is the output of convolutional layers 434 b (asindicated by the skip connection 442) and 436 c. The output ofconvolutional layer 434 b has a higher resolution than that of layer 436c. As another example, the input to the average unpooling layer 439 isthe output of convolutional layers 432 b (as indicated by the skipconnection 442) and 438 b. The output of convolutional layer 432 b has ahigher resolution than that of layer 438 b. In this way, high frequencyinformation that is lost through the application of pooling layers alongthe down-sampling path is re-introduced (and not lost) as input to theunpooling layers along the up-sampling path. Although not expresslyshown in FIG. 4A, a non-linearity layer (e.g., a rectified linear unitor ReLU, sigmoid, etc.) may be applied after one or more (e.g.,convolutional) layers shown in the architecture 430. In addition, batchnormalization may be applied at one or more points along thearchitecture 430 (e.g., at the input layer).

FIG. 4B illustrates a specific example of the architecture of the neuralnetwork shown in FIG. 4A. As shown in FIG. 4B, all of the convolutionallayers apply a 3×3 kernel. In the down-sampling path, the input at eachlevel is processed by repeated application of two (or three at thebottom level) convolutions with 3×3 kernels, each followed by anapplication of a non-linearity, an average 2×2 pooling operation withstride 2 for down-sampling. At each down-sampling step the number offeature channels is doubled from 64 to 128 to 256. The number of featurechannels is also doubled from 256 to 512 at the bottom layer. In theup-sampling path, the data is processed by repeated up-sampling of thefeature maps using an average unpooling step that halves the number offeature channels (e.g., from 256 to 128 to 64), concatenating with thecorresponding feature map from the down-sampling path and one or moreconvolutional layers (using 3×3 kernels), each followed by applicationof a non-linearity. The last convolutional layer 440 c reduces thenumber of feature maps to 2.

In some embodiments, a neural network for suppressing RF interference ornoise may include “spectral pooling” and “spectral unpooling” layers, asshown, for example, in FIG. 4C that illustrates the architecture 450 ofa CNN having a “U” structure and spectral pooling and unpooling layersinstead of the average pooling and unpooling layers.

As shown in FIG. 4C, in the down-sampling path, convolutional layers 452a and 452 b are applied to input 451. A spectral pooling layer 453 isthen applied to the output of convolutional layer 452 b, andconvolutional layers 454 a and 454 b are applied to the lower-resolutiondata produced by the spectral pooling layer 453. Another spectralpooling step 455 is applied to the output of convolutional layer 454 b,and convolutional layers 436 a, 436 b, and 436 c are applied to theoutput of spectral pooling layer 455. In the up-sampling path, theoutput of convolutional layer 456 c is processed by the spectralunpooling layer 457 whose output is in turn processed by convolutionallayers 458 a and 458 b. The output of convolutional layer 458 b isprocessed by spectral unpooling layer 459, whose output is processed byconvolutional layers 460 a-c to generate output 465. A spectral poolinglayer may be implemented by simply removing higher spatial frequencycontent from the data, which may be implemented efficiently since thedata may be already in the spatial frequency domain, and a DiscreteFourier Transform (DFT) is not needed.

The architecture 450 also includes skip connections 461 and 462. Thus,the input to spectral unpooling layer 457 is the output of convolutionallayers 454 b and 456 c (with the output of layer 454 b including higherfrequency content than the output of layer 456 c). The input to spectralunpooling layer 459 is the output of layers 452 b and 458 b (with outputof layer 452 b including higher frequency content than output of layer458 b).

The architecture 450 may be implemented in a manner analogous to that ofarchitecture 430 in FIG. 4B. For example, 3×3 kernels may be used andthe number of feature channels may increase from 64 to 128 to 256 to 512along the down-sampling path and decrease from 512 to 256 to 128 to 64and to 2 along the up-sampling path. However, any other suitableimplementation (e.g., number of feature channels, kernel size, etc.) maybe used, as aspects of the technology described herein are not limitedin this respect.

FIG. 4D illustrates an example architecture of spectral unpooling layer457 part of architecture 450. In FIG. 4D, the output 480 of spectralunpooling layer 457 is generated from two inputs: (1) high resolutionfeatures 470 provided via skip connection 462 (from output ofconvolutional layer 452 b); and (2) low resolution features 474 providedas output from convolutional layer 458 b. The high resolution features470 include higher (spatial) frequency content than the low resolutionfeatures 474. As one specific example, the low-resolution features 474may include one or more (e.g., 128) feature channels each comprising64×64 complex values and the high-resolution features may include one ormore (e.g., 64) feature channels each comprising 128×128 complex values.A high-resolution 128×128 feature channel and a correspondinglow-resolution 64×64 feature channel may be combined by: (1) zeropadding the 64×64 feature channel to obtain a 128×128 zero-padded set ofvalues; and (2) adding the high resolution 128×128 feature channel(weighted by weights 472) to the 128×128 zero-padded set of values(weighted by weights 478).

In the illustrated embodiment, the spectral unpooling layer 457 combinesthe high resolution features and low resolution features 474 by: (1)zero padding the low resolution features 474 using zero padding block476; and (2) computing a weighted combination of the zero-paddedlow-resolution features (weighted using weights 478) with the highresolution features (weighted by weights 472). In some embodiments, theweights 472 and 478 may be set manually, in others they may be learnedfrom data.

The neural networks 220, 224, and 226 may be implemented in any suitabledomain. For example, in some embodiments, each of one or more of thesenetworks may be applied in the sensor domain, spectral domain, logspectral domain, time domain, spatial frequency domain, wavelet domain,and/or any other suitable domain, as aspects of the technology describedherein are not limited in this respect.

Neural Network Training

The neural network models described herein may be trained using anysuitable neural network training algorithm(s), as aspects of thetechnology described herein are not limited in this respect. Forexample, in some embodiments, the neural network models described hereinmay be trained by using one or more iterative optimization techniques toestimate neural network parameters from training data. For example, insome embodiments, one or more of the following optimization techniquesmay be used: stochastic gradient descent (SGD), mini-batch gradientdescent, momentum SGD, Nesterov accelerated gradient, Adagrad, Adadelta,RMSprop, Adaptive Moment Estimation (Adam), AdaMax, Nesterov-acceleratedAdaptive Moment Estimation (Nadam), and AMSGrad.

In some embodiments, training data for training a neural network may begenerated synthetically from available MR images. In particular, in someembodiments, magnitude MR images (phase information is typicallydiscarded) may be used to generate corresponding spatial frequency dataand the resulting (spatial frequency data, MR image) pairs may be usedto train a neural network model, including any of the neural networkmodels described herein, for example, by using any of theabove-described algorithms.

In some embodiments, the process of synthesizing spatial frequency datafrom MR image data for training a neural network may take into accountone or more characteristics of MRI system that will collect patient datathat the neural network is being trained to process once the neuralnetwork is deployed. Non-limiting, examples of such characteristicsinclude, but are not limited to, size of the field of view of the MRIsystem, sampling patterns to be used by the MRI system during imaging(examples of various sampling patterns are provided herein), number ofRF coils in the MRI system configured to detect MR data, geometry andsensitivity of RF coils in the MRI system, pulse correlation amongsignals received by the RF coils of the MRI system, RF interference(external and internal) that the MRI system is expected to experienceduring operation, RF noise (e.g., from the MR signal receive chain) thatthe MRI system is expected to experience during operation, pulsesequences to be used during imaging, and field strength of the MRIsystem.

Using characteristics of the MRI system that will collect patient datato generate training data allows for the neural network to learn thesecharacteristics and use them to improve its performance on tasks in thereconstruction pipeline. Moreover, this approach allows the trainedneural network models to reconstruct MR images of comparably highquality based on sensor data acquired using MRI hardware and softwarethat produces comparatively lower quality sensor measurements due tovarious hardware and software characteristics (including constraints andimperfections).

FIGS. 5A-5C show an illustrative diagram of a process 500 for generatingtraining data from MR images for training the neural network modelsdescribed herein, in accordance with some embodiments of the technologydescribed herein. The process 500 starts with a magnitude MR volume 502using various specified characteristics of an MRI system generatesspatial frequency data 550, which includes spatial frequency datacollected multiple times (N_(avg) times in this example) by each ofmultiple RF cols of the MRI system (8 in this example). Process 500 maybe performed by any suitable computing device(s) and, in someembodiments, may be performed in a cloud computing environment, forexample.

In some embodiments, process 500 may be repeated multiple times bystarting from the same MR volume 502 to generate different spatialfrequency data 550, since multiple portions of the process 500 can bemade to vary across different runs since these portions sample certainvariations and parameters at random. Repeating process 500 multipletimes by starting from the same MR volume, but varying the processparameters (e.g., transformations applied to the image at acts 508, 510,and 512) enables the generation of multiple training data pairs from asingle MR volume, which is a type of data augmentation that not onlyincreases the diversity and coverage of the training data, but alsoreduces the demand to obtain greater amounts of real-world MRI imagesneeded for training, which can be expensive, time-consuming, andimpractical.

As shown in FIGS. 5A-5C, process 500 begins by accessing a referencemagnitude MR volume 502. The MR volume 502 may comprise one or multipleimages. Each of the image(s) may represent an anatomical slice of asubject being imaged. The MR volume 502 may include one or moremagnitude images obtained by a clinical MRI system. In some embodiments,for example, the MR volume 502 may be obtained from one or morepublically-accessible databases (e.g., the Human Connectome Project)and/or data associated with one or more publications. The MR volume 502may include brain MR images. Additionally or alternatively, the MRvolume 502 may include MR images of other body parts. The MR volume 502may be represented mathematically as x₀∈

×

×

, where N_(x) ₀ ×N_(y) ₀ ×N_(z) ₀ are the dimensions of the volume(e.g., in pixels).

Next, at 504, desired field of field view FOV(FOV_(x), FOV_(y), FOV_(z))and image resolution (N_(x), N_(y), N_(z)) may be specified, and at 506the MR volume 502 may be cropped and/or resampled to obtain an updatedMR volume x′ having the desired field of view and image resolution, suchthat x′∈

^(N) ^(x) ^(×N) ^(y) ^(×N) ^(z) .

Next, in some embodiments, the updated MR volume x′ may be furthermodified, at 512, by the application of one or more transformations T(x)(generated at 508) and/or application of a histogram augmentationfunction I(x) (generated at 510) to obtain the updated MR volumex″(r)=I(x′(T(r))). Such modifications permit generating multipledifferent training examples from a single underlying MR volume (i.e., MRvolume 502), which is a type of training data augmentation, as describedabove.

In some embodiments, the transformation(s) T(x) (generated at 508) mayinclude one or more 2D or 3D rigid transformations, one or more 2D or 3Daffine transformations (e.g., one or more translations, one or morerotations, one or more scalings) and/or one or more 2D or 3D non-rigidtransformations (e.g., one or more deformations). In some embodiments,each such transformation may be implemented by using a data augmentationmatrix (e.g., a 3×3 matrix for a rigid transformation, a 4×4 matrix foran affine transformation, and a dense deformation grid (e.g., of thesame dimensionality as the MR volume) for a non-rigid transformation).

In some embodiments, an affine transformation T(x) may be generated atrandom at 508 to simulate a realistic variation of how differentpositions and orientations of a patient's anatomy may be positionedwithin the MRI system. For example, if the field of view of the image is22 cm, transformations sampled at 508 may translate the MR volume by adistance of up to 5 cm and/or rotate the MR volume by up to 30 degreesalong the axial angle. A non-rigid transformation T(x) may be generatedat random at 508 to simulate the effect of inhomogeneity of the B₀field, eddy currents and/or encoding error of the MRI system.

In some embodiments, the histogram augmentation function I(r) generatedat 510 may be used to change the intensity variations in regions of theimage to simulate various effects, including, but not limited to theeffect of RF coil correlation and/or to provide different contrasts thatmay occur in multi-echo pulse sequences.

Next, at acts 514, 516, and 518, synthetic phase is generated from alinear combination of spherical harmonic basis functions to generate thetarget complex-valued volume x 520. In some embodiments, coefficientsα_(i) of N spherical harmonic basis functions Y_(i) are sampled, at 514,at random to generate a phase image, at 516, according to: θ=Σ_(i=1)^(N)α₁Y_(i). In turn, the complex-valued target vole 520 may be givenby: x=x″(r)e^(iθ). In some embodiments, the number of sphericalharmonics is selected by the user—the greater the number, the morecomplex the resulting phase. In some embodiments, the range of valuesfor each spherical harmonic coefficient α_(i) may be set by user, forexample, empirically.

Next, after the target image 520 is generated, act 525 (which includesacts 522-544 is repeated) multiple times (N_(avg) times in this example)to generate multiple sets of spatial frequency data, each set includingspatial frequency data for N_(coil) RF coils (8 in this example). Withinact 525, first sequence specific augmentation is performed at acts 522and 524.

In some embodiments, one or more transformations may be generated, at522, at random, to apply to target MR volume 520, and subsequently beapplied to the target MR volume at 524. Generating the transformations,at 522, may include: (1) generating, at 522 a, RF artefacts (e.g.,internal RF interference, noise) to simulate the types of RF artefactsthat may be expected to be observed during a particular pulse sequence;and (2) generating, at 522 b, one or more affine or non-rigidtransformations to simulate the effect of patient motion during aparticular pulse sequence (inter-volume motion).

Next, at acts 526 and 528, an RF coil sensitivity profile is generatedfor each of the N_(coil) RF coils to obtain multiple RF coil sensitivityprofiles S_(i), i=1 . . . N_(coil). Each generated RF coil sensitivityprofile S_(i) is complex-valued, with the magnitudes generated at act526 using one or more RF coil models and with the phases generated(e.g., randomly) at 528. The resulting RF sensitivity profiles areapplied to the MR volume (e.g., to the result of performing, at 524,pulse sequence specific augmentation on target MR volume 520) to obtainmultiple MR volumes, each of the multiple MR volumes obtained byapplying a respective RF coil sensitivity profile to the MR volumeresulting at the output of 524.

The RF coil model used at 524 may be of any suitable type. For example,in some embodiments, the RF coil model used at 526 may be aphysics-based RF coil model, which may be configured to calculate thesensitivity of a particular RF coil given its geometry. Thephysics-based model may be performed for multiple coils simultaneouslyto determine any RF coil coupling and/or inductance effects (e.g., theresults of that calculation may be used at 532, as discussed below). Inother embodiments, the RF coil model may be a statistical model having aGaussian profile for the amplitude and smooth complex phase. In yetother embodiments, a non-uniform map having the same dimension as eachvolume slice may be employed, where each pixel is weighted by a smoothamplitude reduction map and noise is added to determine an overallreduction in SNR that is to be applied.

Next at 532, a coil correlation matrix L′ may be determined. This matrixmay model the effect of RF coil coupling and/or inductance. The coilcorrelation matrix L′ may be determined based on a model of RF coilinductance (e.g., a physics-based model as described above). Next, at534, the coil correlation matrix may be perturbed (e.g., randomly) toobtain a coil correlation matrix L. At 536, the coil correlation matrixL is applied to the pixel data.

Next, at 538 and 540, correlated Gaussian noise is generated and added,at 542, to the multiple MR volumes produced at 536. In some embodiments,the Gaussian noise may be generated by: (1) determining, at 538, a noiselevel σ_(i) for each of the coils; and (2) generating, at 540, Gaussiannoise having the covariance of LDL^(T), where D is a diagonal matrixwith D_(ii)=σ_(i), and L is the coil correlation matrix determined at534.

Next, at 544, a k-space sampling trajectory is selected. The samplingtrajectory may be of any suitable type. It may be Cartesian ornon-Cartesian (e.g., radial, spiral, rosette, variable density,Lissajou, etc.). Next, at 546, noise δk(t) is added to samplingtrajectory k(t). The noise may be added to simulate for various MRIsystem imperfections and/or any other reason. Next, at 548, anon-uniform Fourier transform is applied to the noise-corruptedcoil-weighted MR volumes produced at 542.

As a last step, at 545, k-space augmentation may be performed to performfurther sequence-specific augmentation. For example, this may be done tomodel them impact of the basebanging artefact in bSSFP (balanced steadstate free precession) sequences or warping artefacts in DWI (diffusionweighted imaging).

The resulting spatial frequency data are then output, at 550. These datamay be used for training any of the neural network models describedherein.

It should be appreciated that the process 500 is illustrative and thatthere are variations thereof. For example, one or more of the acts ofprocess 500 may be omitted, in some embodiments. For example, whengenerating data for training a neural network to operate on datacollected by an MRI system having a single RF coil, acts 532-542 may beomitted, in some embodiments. As another example, one or more of theaugmentation acts (e.g., k-space augmentation at 545) may be omitted, insome embodiments.

Unsupervised Learning with Low-Field Data

As described herein, including above with reference to FIG. 5, in someembodiments, neural network models developed by the inventors anddescribed herein may be trained using training data generated fromexisting high-field image data. Indeed, a training dataset of (sensorinput data, image) pairs may be generated by, for each pair, startingwith a high-field source image x_(h) and using a model of the “forwardprocess” (e.g., the forward process described with reference to FIG. 5)to generate input sensor data y_(h), thereby forming the pair (y_(h),x_(h)). However, the inventors have recognized that generating trainingdata from high-field data, training neural network models on suchtraining data, and then applying the trained neural network models toprocess low-field data (e.g., data collected using an MRI system havinga B0 field strength between 0.02 T and 0.2 T) results in worseperformance as compared to when the trained neural network models areapplied to the type of high-field data that their training dataset wasgenerated from. This problem is often referred to as “domain shift.”

One way of mitigating domain shift is to a train neural network fromlow-field data when the trained neural network is to be applied tolow-field data and to train neural networks from high-field data whenthe trained neural network is to be applied to high-field data. However,there is simply insufficient low-field MR data from which to train andthe existing data is noisy, making it very difficult to generatelow-field (k-space data, image) pairs. As a result, training a neuralnetwork from purely low-field data is not always possible.

The inventors have recognized that this problem may be addressed bytraining the neural network with data pairs derived from high-field data(as above), but also augmenting the loss function with losses computedwith respect to available low-field images. The key insight is that,even if a neural network were trained using high-field data, theresulting network should reconstruct the same image from both: (1) afirst set of low-field k-space data; and (2) a second set of low-fielddata obtained by applying a geometric transformation to the first set oflow-field k-space data, where the image reconstruction should beinvariant under the transformation.

For example, rotating the input sensor domain data along by a particularrotation angle, should simply cause the reconstructed image to berotated by the same angle. Other non-limiting examples of geometrictransformations with respect to which the image reconstruction should beinvariant include linear shift, phase shift, conjugation, and flipping.

Accordingly, in some embodiments, the loss function for training aneural network model for performing image reconstruction (e.g., neuralnetwork model 212), may incorporate a loss applied on low-field data.Formally, let x∈C^(N) denote a complex-valued MR image to bereconstructed, represented as a vector with N=N_(x)N_(y) where N_(x) andN_(y) are width and height of the image. Let y∈C^(M)(M<<N) represent theunder-sampled k-space measurements. Denote the image reconstruction by atrained neural network f that generates x from y. Then, in someembodiments, the neural network may be trained using the following lossfunction:

_(self) =E _(y˜p(y) _(h) ₎[

₁]+E _(y˜p(y))[

₂+

₃],

where the constituent loss functions are given by:

₁ =∥f(y _(h))−x _(h)∥

₂ =∥f(y)−T ⁻¹(f(T(y)))∥

₃=

(f(y)).

Here, the loss function

₁ penalizes errors in reconstruction of high-field images; it is basedon the available data pairs generated from high-field images. The lossfunction

₂ penalizes errors between image reconstructions of a data set and ageometric transformation thereof, where the reconstruction should beinvariant to action by the geometric transformation. The loss function

₃ implements a regularization term, such as total variation norm, whichis typically applied in compressed sensing type reconstructions. In someembodiments, the loss function

_(self) may be a weighted combination of the individual loss functions

₁,

₂ and

₃.

Additionally or alternatively, another way to generate a trainingdataset is to use source images of higher quality x_(o), such as thoseobtained from low-field scanners, but using more data samples. Thesensor data can be obtained directly by collecting the scannermeasurements y_(o). The higher quality data x_(o) and input data x arerelated by a mask in the sensor domain, i.e. y=M·y_(o). The trainingloss can then be written as:

₄ =∥f(y)−x _(o)∥.

Motion Correction and Alignment

As described herein, multiple MR images of a single slice of a patient'sanatomy may be acquired in order to enhance MR image quality byaveraging the multiple MR images to increase the resulting SNR. Multiplesets of images covering a same volume of the patient's anatomy (e.g., avolume containing multiple slices of the patient's anatomy) may beacquired and averaged for the same reason. However, performing multipleacquisitions (e.g. of the same slice and/or of the same volume)increases the overall total acquisition time, which in turn increasesthe likelihood that the patient moves during imaging. On the other hand,patient motion causes misalignment between the multiple acquisitions.Averaging such misaligned acquisitions would not improve SNR as isdesirable and, instead, may degrade the images, for example, throughblurring.

As described herein, the inventors have developed deep learningtechniques for aligning sets of images obtained by multiple acquisitionsof the same slice and/or volume. In some embodiments, the deep learningtechniques involve using a cascade of two or more neural networksconfigured to estimate a transformation (e.g., a non-rigid, an affine, arigid transformation) between two sets of MR images (each set having oneor multiple MR images), and aligning the two sets of images using theestimated transformation. In turn, the two sets of images may beaveraged to obtain a combined set of images having a higher SNR than thesets of images themselves.

In some embodiments, the estimated transformation may indicate one ormore rotations and/or translations to align the two sets of images. Insome embodiments, the deep learning techniques described herein may beused as part of neural network 234 part of post-reconstruction neuralnetwork 214, as described herein including in connection with FIG. 2C.

Accordingly, some embodiments provide for a system and/or a method forgenerating MR images of a subject from MR data obtained by an MRIsystem. In some embodiments, the method includes: (1) obtaining firstinput MR data obtained by imaging the subject using the MRI system; (2)obtaining second input MR data obtained by imaging the subject using theMRI system; (3) generating a first set of one or more MR images from thefirst input MR data (e.g., by reconstructing the first set of MR imagesfrom the first input MR data); (4) generating a second set of one ormore MR images from the second input MR data (e.g., by reconstructingthe second set of MR images from the second input MR data); (5) aligningthe first set of MR images and the second set of MR images using aneural network model to obtain aligned first and second sets of MRimages, the neural network model comprising a first neural network and asecond neural network; (6) combining the aligned first and second setsof MR images to obtain a combined set of one or more MR images; and (7)outputting the combined set of one or more MR images.

In some embodiments, the aligning may include: (a) estimating, using thefirst neural network, a first transformation (e.g., a first rigidtransformation expressed as a combination of one or more translationsand/or one or more rotations) between the first set of MR images and thesecond set of MR images; (b) generating a first updated set of MR imagesfrom the second set of MR images using the first transformation; (c)estimating, using the second neural network, a second transformation(e.g., a second rigid transformation expressed as a combination of oneor more translations and/or one or more rotations) between the first setof MR images and the first updated set of MR images; and (d) aligningthe first set of MR images and the second set of MR images at least inpart by using the first transformation and the second transformation(e.g., by using a composition of the estimated two transformations. Insome embodiments, a software program may perform the above-describedacts. Alternately, one or more of these acts may be implemented usinghardware. Accordingly, the MR image generation techniques describedherein may be implemented using hardware, software, or any suitablecombination of hardware and software.

In some embodiments, obtaining the second input MR data may be performedafter obtaining the first input MR data. For example, the first input MRdata may contain MR data for each of multiple slices of a volume, thesecond input MR data may contain MR data for the same slices of the samevolume, and all of the second input MR data may be acquired after thefirst input MR data. In other embodiments, the acquisition of the firstand second input MR data may be interlaced: MR data for a first slice isobtained twice (the first instance will be part of the first set ofinput MR data and the second instance will be part of the second set ofinput MR data), then MR data for a second slice is obtained twice (thefirst instance will be part of the first set of input MR data and thesecond instance will be part of the second set of input MR data), thenMR data for a third slice is obtained twice (the first instance will bepart of the first set of input MR data and the second instance will bepart of the second set of input MR data), and so on.

In some embodiments, generating the first updated set of MR images fromthe second set of MR images, comprises applying the first transformationto the second set of MR images. The first transformation may, forexample, be a rigid transformation. In some embodiments, the firsttransformation may include one or more translations and/or one or morerotations determined by the first neural network. The translations maydescribe one or more translations along the x-, y-, and/or z-directions.The rotations may describe one or more rotations about the x, y, and/orz axes. In some embodiments, the rotations may be described by rotationangles (e.g., Euler rotation angles). In some embodiments, estimatingthe first transformation may be performed at least in part by using thealigning is performed by at least one graphics processing unit (GPU)part of the MRI system.

In some embodiments, generating the first updated set of MR imagesadditionally comprises interpolating results of applying the firsttransformation to the second set of MR images. For example, a pixelvalue of an image of the second set of MR images may be, after atransformation is applied, located “between” pixels of the pixel arrayof the transformed MR image. Pixel values of the transformed MR imagemay be interpolated based on, for example, an average of signal valueswithin a vicinity of each pixel or in any other suitable way, as aspectsof the technology described herein are not limited in this respect.

In some embodiments, aligning the first set of MR images and the secondset of MR images may comprise calculating a composed transformation bycomposing the first and second transformations. For example, in someembodiments, the composed transformation may be obtained by composingthe rotation and translation parameters of the first and secondtransformations. The composed transformation may be applied to thesecond set of MR images to obtain a set of MR images aligned to thefirst set of MR images. Alternatively, in some embodiments, aligning thefirst set of MR images and the second set of MR images may compriseobtaining a set of MR images aligned to the first set of MR images fromthe first set of updated MR images. In some embodiments, the aligningmay be performed by at least one processor part of the MRI system.

In some embodiments, the neural network model additionally includes athird neural network. In such embodiments, the aligning of the first setof MR images and the second set of MR images further comprises: (e)generating a second updated set of MR images from the first updated setof MR images using the second transformation; (f) estimating, using thethird neural network, a third transformation between the first updatedset of MR images and the second updated set of MR images; and (g)aligning the first set of MR images and the second set of MR images atleast in part by using the first transformation, the secondtransformation, and the third transformation (e.g., by composition of atleast the first, second, and third transformations).

In some embodiments, the first neural network comprises one or moretwo-dimensional (2D) convolutional layers. In some embodiments, thefirst neural network comprises one or more three-dimensional (3D)convolutional layers configured to simultaneously process data inmultiple images of the first set of MR images (e.g., to processvolumetric data).

In some embodiments, the first set of MR images may consist of one imageand the second set of MR images may consist of one MR image. In suchembodiments, the first set of MR images and the second set of MR imagesmay describe a single slice of the imaging volume. Alternately, thealignment of first and second sets of MR images may be performed by theneural network an image-at-a-time (e.g., by comparing single MR imagesrather than comparing multiple MR images that describe the entireimaging volume).

In some embodiments, combining the aligned first and second sets of MRimages comprises averaging images of the aligned first and second setsof MR images. For example, images of the aligned first and second setsof MR images corresponding to a same slice of the imaging volume may beaveraged to increase SNR in the resulting combined image.

FIG. 6 is a diagram of an example neural-network based architecture 600for aligning one or more MR images, in accordance with some embodimentsof the technology described herein. As can be appreciated from FIG. 6,the architecture 600 is cascaded because it comprises a cascade ofneural networks, each configured to estimate a respective transformationbetween two sets of MR images. Since the transformation may account forpatient motion during collection of the two sets of MR images, theseneural networks are termed motion estimation networks.

In the embodiment of FIG. 6, the cascaded architecture 600 includes twomotion estimation networks: first motion estimation network 610 andsecond motion estimation network 620 configured to determine motiontransformation parameters (e.g., rotation and/or translation parameters)between reference volume 602 and moving volume 604. Though it should beappreciated that, in other embodiments, the cascaded architecture mayinclude more than two motion estimation neural networks (e.g., three,four, five, six, seven, eight nine, ten, etc.), as aspects of thetechnology described herein are not limited to using exactly two motionestimation networks.

The inventors have appreciated that using a cascade of multiple neuralnetworks to estimate a series of transformations to align the sets ofimages may lead to improved performance relative to the implementationwhere only one motion estimation neural net is used because a singletransformation may not achieve a perfect alignment, but a series oftransformations, each aligning a moving volume successively closer tothe reference volume, may achieve a much higher degree of alignment.Though it should be appreciated that, in some embodiments, a singlemotion estimation neural network may be used.

In some embodiments, the reference volume 602 may include a set of oneor more MR images generated based on a first set of MR data obtained byimaging a patient using the MRI system. In some embodiments, the set ofMR images may be real-valued images (phase information may bediscarded). For example, the reference volume 602 may include multipleMR images, each of which corresponds to a different volumetric slice ofthe imaged patient (e.g., the multiple MR images may include multiplesagittal slices, multiple axial slices, or multiple coronal slices)obtained from a first instance of an MR imaging protocol (e.g., a seriesof one or more pulse sequences for imaging the patient). In someembodiments, the reference volume 602 may be provided as an input toeach of the motion estimation networks 610 and 620 of the cascadedarchitecture 600.

In some embodiments, the moving volume 604 may include a set of one ormore MR images generated based on a second set of MR data obtained byimaging a patient using the MRI system. For example, the moving volume604 may include MR images each of which corresponds to a differentvolumetric slice of the patient (e.g., the MR images may includemultiple sagittal slices, multiple axial slices, or multiple coronalslices), and each of the images in the moving volume 604 may have acorresponding image included in reference volume 602. In someembodiments, the moving volume 604 may be used as an input of the firstmotion estimation network 610 and the first estimated parameterresampler (EPR) 614, as described below.

In some embodiments, first motion estimation network 610 may be a neuralnetwork configured to take two sets of MR images (e.g., reference volume602 and moving volume 604) as input and output estimated transformationparameters (e.g., first transformation parameters 612), which describe atransformation for aligning the moving volume 604 to the referencevolume 602 (the misalignment being caused, for example, by patientmovement during imaging).

In some embodiments, the first motion estimation network 610 may be aconvolutional neural network having one or more convolutional layers,one or more transpose convolutional layers, one or more non-linearitylayers, and/or one or more fully connected layers. In some embodiments,the network 610 may be a 2D convolutional neural network or a 3Dconvolutional neural network. An example architecture of network 610 isdescribed herein including with reference to FIG. 7.

In some embodiments, the first transformation parameters 612 output byfirst motion estimation network 610 may include parameters of a rigidtransformation for aligning the reference volume 602 and the movingvolume 604 to one another. For example, the first transformationparameters 612 may include one or more translation parameters todescribe translation along x-, y-, and/or z-directions. Alternatively oradditionally, the first transformation parameters 612 may includerotation angles (e.g., Euler rotation angles) describing rotation aboutthe x, y, and/or z axes.

Next, as shown in FIG. 6, the first transformation parameters 612 areused to transform the moving volume 604 to obtain an updated movingvolume 606. This transformation may be performed by Estimated ParameterResampler 614. For example, the first transformation parameters 612 mayinclude one or more rotation and/or translation parameters, and the EPR614 may transform the moving volume 604 by applying one or morerotations and/or translations defined by the parameters 612 to themoving volume 604.

In some embodiments, generating the updated moving volume 606 may alsoinclude interpolating one or more points within the first updated set ofMR images of the updated moving volume 606. As an example, each MR imageof the moving volume 604 is formed from an array of magnitude values,each magnitude value being associated with a pixel of the MR image. Whena rotation translation is applied to an MR image, the magnitude valuesmay no longer cleanly align with the pixel array of the updated MR image(e.g., the magnitude may correspond to a location “between” arraylocations, pixels at the edge of the image may be cut off or missing).Interpolation may therefore be used to assign magnitude values to eachpixel of the array forming the updated MR image. Any suitable type ofinterpolation technique may be used, as aspects of the technologydescribed herein are not limited in this respect.

Next, the reference volume 602 and the updated moving volume 606 areprovided as input to the second motion estimation network 620. Secondmotion estimation network 620 may be configured to take in two sets ofMR images (e.g., reference volume 602 and updated moving volume 606) andoutput estimated transformation parameters (e.g., transformationparameters 622) which describe an estimated magnitude and type of“motion” represented by the differences between reference volume 602 andupdated moving volume 606.

In some embodiments, the network 620 may be a convolutional neuralnetwork having one or more convolutional layers, one or more transposeconvolutional layers, one or more non-linearity layers, and/or one ormore fully connected layers. In some embodiments, the network 610 may bea 2D convolutional neural network or a 3D convolutional neural network.In some embodiments, the second motion estimation network 620 may havethe same architecture as the first motion estimation network 610, butwith different parameter values since it is trained to perform adifferent task (correcting a much smaller misalignment than the firstmotion estimation network). In other embodiments, the second motionestimation network 620 may have a different architecture (e.g.,different number of convolutional layers, different convolutional kernelsize, different number of features, different non-linearity, and/or anyother suitable difference).

As shown in FIG. 6, the second motion estimation network 620 outputssecond transformation parameters 622. In some embodiments, theparameters 622 include parameters of a rigid transformation betweenreference volume 602 and updated moving volume 606. For example, theparameters 622 may include one or more translation parameters todescribe translation along x-, y-, and/or z-directions. Alternatively oradditionally, the first transformation parameters 612 may includerotation angles (e.g., Euler rotation angles) describing rotation aboutthe x, y, and/or z axes.

In some embodiments, an output of the cascaded architecture 600 mayinclude a final transformed volume (not pictured). In the example ofcascaded architecture 600, as depicted in FIG. 6, the final transformedvolume is generated after second EPR 624 resamples updated moving volume606. The final transformed volume may include the cumulativetransformations and interpolations as applied by the one or more motionestimation networks as the moving volume has been updated throughcascaded architecture 600.

In some embodiments, the cascaded architecture 600 may alternatively oradditionally output the transformation parameters (e.g., transformationparameters 614 and 622) determined by its constituent motion estimationnetworks. The transformations defined by these parameters may becomposed, and the composed transformation may be applied to the movingvolume 604, with an interpolation step optionally following, to obtain avolume that is aligned with reference volume 602.

As one non-limiting example, the transformation parameters {R₁, . . . ,R_(n), c₁, . . . , c_(n)} may be used to generate a composedtransformation according to

T _(final) =T _(n) *T _(n−1) * . . . *T ₁

where T_(i)=[R_(i)|c_(i); 0|1] is a 4×4 transformation matrix and “*” isa matrix multiplication. The composed transformation, T_(final), maythen be applied to moving volume 604, with an interpolation stepoptionally following, to obtained a volume that is aligned withreference volume 602.

In some embodiments, the first motion estimation network 610 may betrained using a loss function based on error in the first transformationparameters 612. However, this approach suffers from multiple drawbacks(e.g., there are multiple transformation parameters that may achieve thesame result and computing the error on a small number of parameters, forexample 6, may not be sufficiently informative for training purposes).Instead, the inventors have recognized that the estimated transformation612 may be used to resample the moving volume 604 and to compute theloss function for training the network 610 based on the image-domainerror between the reference volume 602 and the resampled moving volume604.

For example, in embodiments where the architecture 600 includes only thenetwork 610, the loss function may be computed by resampling MR imagesof moving volume 604 based on the first transformation parameters 612.The resampling may be performed by first EPR 614. The loss functionwould then be given by:

L(θ)=∥V _(ref)−EPR(NN(V _(mov)|θ))∥₂

where θ is the network parameter to be optimized during training,V_(ref) is the reference volume (e.g., reference volume 602), V_(mov) isthe moving volume (e.g., moving volume 604), and NN(V_(mov)|θ) is theoutput of the neural network (e.g., the output of first motionestimation network 610) for a specified V_(mov) and θ.

When the architecture 600 includes multiple (say n) motion estimationnetworks (as is the case for FIG. 6), a different loss function may beused as described below, the loss function, L_(n)(θ) may be used, whichis calculated based on the resampling performed by the EPRs (e.g., firstEPR 614 and EPR 624) according to:

L _(n)(θ)=∥V _(ref)−EPR(NN _(n)( . . . (EPR(NN ₂(EPR(NN ₁(V _(mov)|θ)))). . . ))∥₂

where θ is the network parameter to be optimized during training,V_(ref) is the reference volume (e.g., reference volume 602), V_(mov) isthe moving volume (e.g., moving volume 604), and NN_(n)(V_(mov)|θ) isthe output of the n^(th) motion estimation network.

FIG. 7 is a diagram 700 of the architecture of an illustrative neuralnetwork 710 for aligning one or more MR images, in accordance with someembodiments of the technology described herein. Neural network 710 maybe used as one or more of the motion estimation networks of cascadedarchitecture 600, as described in connection with FIG. 6.

In some embodiments, neural network 710 may be configured a first set ofMR images 702 and a second set of MR images 704. For example, inembodiments where motion estimation network 710 is used as first motionestimation network 610 of cascaded architecture 600, the first set of MRimages 702 may be reference volume 602 and the second set of MR images704 may be moving volume 604. As another example, in embodiments whereneural network 710 is used as a subsequent motion estimation network(e.g., second motion estimation network 620), the first set of MR images702 may be reference volume 602 and the second set of MR images 704 maybe an updated moving volume (e.g., updated moving volume 606) generatedby an EPR (e.g., EPR 615).

In some embodiments, neural network 710 may be a convolutional neuralnetwork comprising one or more convolutional layers 712. For example,convolutional layers 712 may be two-dimensional (2D) convolutionallayers. In such embodiments, neural network 710 may be configured toprocess individual, 2D MR images (e.g., representing a single volumetricslice). The processing of an entire imaging volume may be performed aslice at a time. Alternately, in some embodiments, convolutional layers712 may comprise three-dimensional (3D) convolutional layers. In suchembodiments, neural network 710 may be configured to simultaneouslyprocess multiple MR images representing an entire imaging volume.

In some embodiments, one or more fully connected layers 714 may beapplied to the output of convolutional layers 712. In some embodiments,the output of convolutional layers 712 may be reshaped into aone-dimensional (1D) vector before the application of the one or morefully connected layers 714. Additionally, in some embodiments, a dropoutlayer (not shown) may be included after one or more (or each) of thefully connected layers 714.

Although not expressly shown in FIG. 7, a non-linearity layer (e.g., arectified linear unit or ReLU, sigmoid, etc.) may be applied after anyof the one or more layers shown in the neural network 710. For example,a non-linearity layer may be applied after one or more (or each) of theconvolutional layers 712. Additionally or alternately, a non-linearitylayer may be applied after one or more (or each) of the fully connectedlayers 714.

In some embodiments, neural network 710 may be implemented as a 3Dconvolutional network having the following architecture:

1. 3D Convolution, kernel size=3×3, stride=1, 8 features, ReLU

2. 3D Convolution, kernel size=3×3, stride=1, 8 features, ReLU

3. 3D Convolution, kernel size=3×3, stride=1, 8 features, ReLU

4. 3D Convolution, kernel size=3×3, stride=2, 8 features, ReLU

5. 3D Convolution, kernel size=3×3, stride=1, 16 features, ReLU

6. 3D Convolution, kernel size=3×3, stride=1, 16 features, ReLU

7. 3D Convolution, kernel size=3×3, stride=1, 16 features, ReLU

8. 3D Convolution, kernel size=3×3, stride=2, 16 features, ReLU

9. 3D Convolution, kernel size=3×3, stride=1, 32 features, ReLU

10. 3D Convolution, kernel size=3×3, stride=1, 32 features, ReLU

11. 3D Convolution, kernel size=3×3, stride=1, 32 features, ReLU

12. 3D Convolution, kernel size=3×3, stride=2, 32 features, ReLU

13. 3D Convolution, kernel size=3×3, stride=1, 64 features, ReLU

14. 3D Convolution, kernel size=3×3, stride=1, 64 features, ReLU

15. 3D Convolution, kernel size=3×3, stride=1, 64 features, ReLU

16. Reshape the volume to a 1D vector

17. Fully Connected Layer to 256 features, RELU

18. Dropout Layer

19. Fully Connected Layer to 256 features, RELU

20. Dropout Layer

21. Fully Connected Layer to 256 features

It may be appreciated that the above neural network architecture is byway of example only, and that neural network 710 may have any othersuitable architecture, as aspects of the technology described herein arenot limited in this respect.

In some embodiments, the fully connected layers may determine relativevalues of rotation, Δ{right arrow over (θ)}, and relative values oftranslation, Δ{right arrow over (t)}, between the first set of MR images702 and the second set of MR images 704. The relative values ofrotation, Δ{right arrow over (θ)}, may comprise estimated rotationangles (e.g., Euler angles) describing rotation of the motion-corruptedset of MR images 704 about the x, y, and/or z axes relative to thereference set of MR images 702. The relative values of translation,Δ{right arrow over (t)}, may comprise estimated translation values(e.g., distances) of the second set of MR images 704 along x-, y-,and/or z-directions relative to the first set of MR images 702.

In some embodiments, motion estimation network 700 may use thedetermined relative values of rotation, Δ{right arrow over (θ)}, and thedetermined relative values of translation, Δ{right arrow over (t)}, toestimate rigid transformation parameters 720. Rigid transformationparameters 720 may describe a rigid transformation that maps the secondset of MR images 704 to the first set of MR images 702. The motionestimation network 700 may, in some embodiments, output rigidtransformation parameters 720 as a set of transformation parameters(e.g., values of rotation angles, values of translations). In someembodiments, the motion estimation network 700 may output rigidtransformation parameters 720 as a composed transformation function.

FIG. 8A is a flowchart of an illustrative process 800 for aligning oneor more MR images, in accordance with some embodiments of the technologydescribed herein. Process 800 may be executed using any suitablecomputing device. For example, in some embodiments, the process 800 maybe performed by a computing device co-located (e.g., in the same room)with an MRI system that obtained the MR data by imaging a subject (orobject). As another example, in some embodiments, the process 800 may beperformed by one or more processors (e.g., one or more GPUs) located onthe MRI system that obtained the MR data. Alternately, in someembodiments, the process 800 may be performed by one or more processorslocated remotely from the MRI system (e.g., as part of a cloud computingenvironment) that obtained the input MR data.

Process 800 begins at act 810, where first input MR data is obtained. Insome embodiments, the first input MR data had been previously obtainedby an MRI system and stored for subsequent analysis, so that it isaccessed at act 810. In other embodiments, the first input MR data maybe obtained by an MRI system (including any of the MRI systems describedherein) as part of process 800.

At act 820, second input MR data is obtained. In some embodiments, thesecond input MR data had been previously obtained by the MRI system andstored for subsequent analysis, so that it is accessed at act 820. Inother embodiments, the second input MR data may be obtained by an MRIsystem (including any of the MRI systems described herein) as part ofprocess 800.

In some embodiments, first input MR data and second input MR data may beobtained by the MRI system as repetitions of similar or same MR imagingprotocols. For example, first input MR data and second input MR data maycorrespond, in some embodiments, to first and second MR imaginginstances of the same imaging volume and/or slice. Patient motion maycause the contents of first and second input MR data to be misaligned inthe image domain (e.g., post-reconstruction).

After obtaining the first and second input MR data, a first set of oneor more MR images and a second set of one or more MR images may begenerated from the first input MR data in act 830 and from the secondinput MR data in act 840, respectively, in accordance with someembodiments of the technology described herein. The first and secondsets of MR images may be generated, for example, by reconstructing thefirst and second input MR data to transform the first and second inputMR data from the spatial frequency domain to the image domain. Thereconstruction may be performed in any suitable way, including linearand non-linear methods. For example, when the spatial frequency domaindata is spaced on a Cartesian grid, the data may be transformed using aninverse 2D Fourier transformation (e.g., using the inverse 2D fastFourier transform). As another example, when the spatial frequencydomain data is under-sampled, the data may be transformed using aninverse non-uniform Fourier transformation, using a neural network model(e.g., reconstruction neural network 212), using compressed sensingand/or any other suitable methods, as aspects of the technologydescribed herein are not limited in this respect.

Next, process 800 moves to act 850, in which the first set of MR imagesand the second set of MR images are aligned using a neural network modelto obtain aligned first and second sets of MR images, in accordance withsome embodiments of the technology described herein. The neural networkmodel may be applied in the image domain and may have any suitablearchitecture, including any of the architectures described herein. Insome embodiments, the processing at act 850 may be performed, asdescribed herein including with reference to cascaded architecture 600and/or neural network 710. In some embodiments, the neural network modelmay comprise multiple neural networks (e.g., as in first motionestimation network 610 and second motion estimation network 620 ofcascaded architecture 600).

In some embodiments, act 850 of process 800 may include one or moreadditional acts to align the first set of MR images with the second setof MR images, as described by the flowchart of FIG. 8B. In someembodiments, a first transformation between the first set of MR imagesand the second set of MR images may be estimated using a first neuralnetwork in act 852. The processing at act 852 may be performed by aneural network having any suitable neural network architecture,including any of the architectures described herein. In someembodiments, the processing at act 852 may be performed as describedherein, including with reference to neural network 710.

In some embodiments, the estimated first transformation may be anysuitable transformation describing a transformation between the firstand second sets of MR images, including any of the transformationsdescribed herein. For example, the first transformation may be a rigidtransformation. In some embodiments, the first transformation maydescribe one or more translations (e.g., along any or each of the x-,y-, and/or z-directions) and/or may describe one or more rotations(e.g., about any or each of the x, y, and/or z axes). In otherembodiments, the first transformation may be an affine or non-rigidtransformation.

After completing act 852, process 800 moves to act 854, where a firstupdated set of MR images is generated from the second set of MR imagesusing the first transformation. In some embodiments, the first updatedset of MR images may be generated by applying the first transformation(e.g., any one of a number of translation and/or rotations) to thesecond set of MR images. In some embodiments, generating the firstupdated set of MR images may include interpolating one or more pixelvalues of the first updated set of MR images.

Next, process 800 moves to act 856, where a second transformationbetween the first set of MR images and the first updated set of MRimages is estimated using the second neural network. The processing atact 856 may be performed by any suitable neural network architecture,including any of the architectures described herein. In someembodiments, the processing at act 856 may be performed in any waydescribed herein, including with reference to neural network 710.

In some embodiments, the estimated second transformation may be anysuitable transformation describing a transformation between the firstset of MR images and the first updated set of MR images, including anyof the transformations described herein. For example, the firsttransformation may be a rigid transformation. In some embodiments, thefirst transformation may describe one or more translations (e.g., alongany or each of the x-, y-, and/or z-directions) and/or may describe oneor more rotations (e.g., about any or each of the x, y, and/or z axes).In some embodiments, the second transformation may be configured tocorrect any misalignment remaining after the application of the firsttransformation to the second set of MR images.

Thereafter, process 800 moves to act 858, where the first set of MRimages and the second set of MR images are aligned at least in part byusing the first transformation and the second transformation. In someembodiments, the first set of MR images and the second set of MR imagesare aligned by generating a second set of updated MR images afterestimating the second transformation. For example, the secondtransformation may be applied to the first updated set of MR images togenerate a second set of updated MR images. In some embodiments,generating the second set of updated MR images may include interpolatingone or more pixel values of the second set of updated MR images.

In some embodiments, the first set of MR images and the second set of MRimages may be aligned by applying a composed transformation to thesecond set of MR images. For example, the neural network model mayoutput one or more transformation parameters (e.g., of the firsttransformation, second transformation, and/or any other transformation)which may be used to generated a composed transformation, as describedherein in connection with FIG. 6.

After acts 852-858 of act 850, process 800 moves to act 860, as shown inFIG. 8A, where the aligned first and second sets of MR images arecombined to obtain a combined set of one or more MR images. In someembodiments, the aligned first and second sets of MR images may becombined by averaging images of the first and second sets of MR images.For example, images corresponding to a same slice of the imaging volumemay be averaged to increase SNR in the resulting MR image. In someembodiments, the averaging may comprise a weighted average. After act860 completes, process 800 moves to act 870 where the combined set of MRimages is output (e.g., saved for subsequent access, transmitted to arecipient over a network, displayed to a user of the MRI system, etc.).

In some embodiments, the above-described networks and methods may beimplemented as a part of a data processing pipeline, such as the examplepipeline 900 of FIG. 9. In some embodiments, the pipeline 900 mayreceive a deep learning model 902 and MR images 904 as inputs. The deeplearning model 902 may be any deep learning model configured to performmotion estimation and/or correction, as described herein. For example,the deep learning model may include any of the motion estimationnetworks described with reference to FIG. 6 or neural network 710. Insome embodiments, the deep learning model 902 may be implemented inpipeline 900 as deep learning module 906.

In some embodiments, the input MR images 904 may be any related MRimages (e.g., series of MR images representing the same imaging volume,series of MR images representing the same slice). In some embodiments,the input MR images 904 may have been previously obtained by an MRIsystem and stored for subsequent analysis, so that the input MR images904 are accessed for input into pipeline 900. In other embodiments, theinput MR images may be obtained by an MRI system (including any of theMRI systems described herein) including one or more processors toimplement pipeline 900.

In some embodiments, pipeline 900 may select, using any suitable method,a first set of MR images from the input MR images 904 to be the set ofreference MR images 908. The pipeline 900 may provide the set ofreference MR images 908 and the remaining MR images of the input MRimages 904 to the deep learning module 906 for processing.

In some embodiments, the deep learning module 906 may align theremaining MR images of the input MR images 904 to the reference MRimages 908. The deep learning module 906 may implement any suitablealignment method to align the remaining MR images of the input MR images904 with the reference MR images 908. For example, the deep learningmodule 906 may implement process 800 to align the images, as describedin connection with FIGS. 8A and 8B.

The deep learning module may output one or more transformations 910based on the reference MR images 908 and the remaining MR images of theinput MR images 904, in some embodiments. The transformations 910 may beoutput as transformation parameters or as a composed transformation. Insome embodiments, the transformations 910 may be any suitabletransformation as described herein. For example, the transformations maybe rigid transformations. In some embodiments, the transformation maydescribe one or more translations (e.g., along any or each of the x-,y-, and/or z-directions) and/or may describe one or more rotations(e.g., about any or each of the x, y, and/or z axes).

In some embodiments, the remaining MR images of the input MR images 904may be resampled by estimated parameter resampler 912 based ontransformations 910. Resampler 912 may use the transformations totransform the input MR images 902 (e.g., as described with reference toEPR 614).

In some embodiments, the pipeline 900 may evaluate at junction 914whether the transformations 910 represent estimated motion that shouldbe corrected. Some transformations 910 may not be a result of patientmotion. For example, the partial volume effect, may result in smallestimated transformations 910 that are not due to patient motion but arean artefact of the MR imaging process. In some embodiments, pipeline 900may evaluate whether transformations 910 are above a certain thresholdvalue. For example, pipeline 900 may evaluate whether a translation isabove a translation threshold value (e.g., a translation of one pixel, atranslation of two pixels, or any suitable threshold value) and/orwhether a rotation is above a rotation threshold value (e.g., a rotationof one degree, a rotation of two degrees, or any suitable thresholdvalue). If the transformations 910 are not greater than the thresholdvalues, pipeline 900 may not correct the remaining MR images of theinput MR images 904.

In some embodiments, pipeline 900 may output registered MR images 916.Registered MR images 916 may include reference MR image 908 andtransformed remaining MR images of the input MR images 904. Transformedremaining MR images of the input MR images 904 may be transformed as apart of deep learning module 906, in some embodiments. Alternately, oneor more transformations based on transformations 910 may be applied toremaining MR images of the input MR images 904 in order to obtaintransformed remaining MR images of the input MR images 904.

Turning to FIG. 10, additional aspects of training neural networksconfigured to perform motion estimation and/or correction are described,in accordance with some embodiments of the technology described herein.It may, in some instances, be difficult to acquire large scale realmotion-corrupted data for training of any of the neural network modelsdescribed herein. Accordingly, in some embodiments, it may be desirableto generate synthetic training data including reference MR images andsynthetic motion-corrupted MR images based on existing datasets 1002 ofMR images. An illustrative process 1000 for generating such synthetictraining dataset is described in connection with FIG. 10 herein.

Process 1000 may be executed using any suitable computing device. Forexample, in some embodiments, the process 1000 may be performed by acomputing device co-located (e.g., in the same room) with an MRI system.As another example, in some embodiments, the process 1000 may beperformed by one or more processors located remotely from the MRI system(e.g., as part of a cloud computing environment).

To generate such synthetic training datasets, a volume may be selectedand loaded in act 1004 from dataset 1002. In some embodiments, only amagnitude portion of the volume may be loaded. After loading theselected volume in act 1004, a random affine transformation matrix T maybe sampled in act 1006. In some embodiments, the random affinetransformation matrix T may be sampled from a number of affinetransformation matrices (e.g., stored in a database) or the randomaffine transformation matrix T may be randomly generated using anysuitable random generation method.

In some embodiments, the sampled random affine transformation matrix Tmay then be applied to the loaded volume in act 1008. The transformedvolume may be stored as a reference volume.

After generating the reference volume in act 1008, the process 1000 mayproceed to acts 1010-1016 to generate the moving volume. In act 1010, arandom rotation matrix R and a random translation vector c may besampled. In some embodiments, the rotational matrix R and the randomtranslation vector c may be sampled from a number of rotation matricesand translation vectors (e.g., stored in a database), or the randomrotational matrix R and the random translation vector c may be randomlygenerated using any suitable random generation method. In act 1012, thesampled rotation matrix R and translation vector c may be applied to thereference volume to generate a moving volume.

To better train the neural network model, it may be desirable to includesynthetic noise in the synthetic training data (e.g., to simulatenon-ideal MR imaging conditions). In act 1014, Gaussian noise may besampled in act 1014. The Gaussian noise may be selected to match thevolume size of the loaded volume. Alternatively or additionally, in someembodiments, noise may be added to the reference volume and the movingvolume by undersampling a percentage of the MR data in k-space. In act1016, the Gaussian noise may be added to the reference volume and themoving volume to form the synthetic training data pair for use by theneural network model.

In some embodiments, additional non-rigid transformations (not pictured)may be applied to the moving volume to simulate pulse sequence-specificdeformations that may be encountered by the neural network. Examples ofsuch non-rigid transformations include dilation of the volume and/orshearing of the volume.

FIGS. 11A, 12A, and 13A show examples of motion-corrupted MR images ofdifferent patients' brains. FIGS. 11A, 12A, and 13A were all acquiredusing a balanced steady-state free precession (bSSFP) pulse sequenceusing a low-field MRI system, as described herein. FIGS. 11B, 12B, and13B show corresponding examples of motion-corrected MR images, themotion correction being performed using motion estimation and correctionmethods as described herein.

FIGS. 14A and 14B show an example of MR images of a phantom unaffectedby motion. The MR images of FIG. 14B have been evaluated using themotion estimation and correction method as described herein, though asno motion was detected by the neural network model, no correction to theMR images was performed.

Self Ensembling

The inventors have developed techniques for improving non-linear MRreconstruction methods using self-ensembling. For example, in thecontext of MR image reconstruction using neural network models,self-ensembling may reduce or remove errors introduced by the neuralnetwork model in each MR image without requiring that additionaltraining of the neural network model be performed.

The idea behind self ensembling is to create one or more variants of theinput MR data (prior to reconstruction) by applying one or moreinvertible functions to the input MR data. Then the original input MRdata and its variant(s) are reconstructed, inverse(s) of the invertiblefunction(s) are applied to the reconstructed variant(s), and theresulting images are averaged.

The self-ensembling techniques described herein may suppress (e.g.,reduce or eliminate) any errors introduced through the neural networkreconstruction, which may result in higher-quality, higher SNR images.The self-ensembling techniques described herein are not limited to beingapplied in embodiments where neural networks are used to perform imagereconstruction and may be applied in the context of any non-linear MRreconstruction method (e.g., compressed sensing).

Accordingly, the inventors have developed techniques for self-ensemblingof MR data. Some embodiments provide for systems and methods forgenerating MR images of a subject from MR data obtained by an MRIsystem. The method comprises: (1) obtaining input MR data obtained byimaging the subject using the MRI system; (2) generating a plurality oftransformed input MR data instances by applying a respective firstplurality of transformations to the input MR data; (3) generating aplurality of MR images from the plurality of transformed input MR datainstances and the input MR data using a non-linear MR imagereconstruction technique; (4) generating an ensembled MR image from theplurality of MR images at least in part by: (a) applying a secondplurality of transformations (e.g., to mitigate the effects of the firstplurality of transformations in the image domain) to the plurality of MRimages to obtain a plurality of transformed MR images; and (b) combiningthe plurality of transformed MR images to obtain the ensembled MR image;and (5) outputting the ensembled MR image. In some embodiments, asoftware program may perform the above-described acts. Alternately, oneor more of these acts may be implemented using hardware. Accordingly,the MR image generation techniques described herein may be implementedusing hardware, software, or any suitable combination.

In some embodiments, applying the first plurality of transformations tothe input MR data comprises applying one or more of a selection oftransformations in the spatial frequency domain. For example, the firstplurality of transformations may include any one of a constant phaseshift transformation, a linear phase shift transformation, a complexconjugation transformation, a rotation transformation, a transposetransformation, and/or a reflection transformation. Applying the firstplurality of transformations to the input MR data may generate aplurality of transformed input MR data instances for use inself-ensembling the input MR data.

In some embodiments, using the non-linear MR image reconstructiontechnique comprises applying a neural network model to the transformedinput MR data instances to obtain the plurality of MR images. Thenon-linear MR image reconstruction technique may be any suitable neuralnetwork model configured to perform MR image reconstruction. Forexample, the neural network model may be reconstruction neural network212, as described in connection with FIGS. 2A and 2C.

In some embodiments, using the non-linear MR image reconstructiontechnique comprises using a compressed sensing (CS) technique. Thenon-linear MR image reconstruction technique may be any suitable CStechnique configured to perform MR image reconstruction. For example,the CS technique may be any one of an iterative soft thresholdingalgorithm (ISTA), a sub-band adaptive iterative soft thresholdingalgorithm (SISTA), fast iterative soft thresholding algorithm (FISTA),energy preserving sampling (ePRESS), exponential wavelet transform(EWT), exponential wavelet transform iterative soft thresholdingalgorithm (EWT-ISTA), exponential wavelet iterative shrinkagethresholding algorithm (EWISTA), exponential wavelet iterative shrinkagethresholding algorithm with random shift (EWISTARS), and/or any othersuitable CS techniques.

In some embodiments, applying the second plurality of transformations tothe plurality of MR images comprises applying the second plurality oftransformations to the plurality of MR images in an image domain. Thesecond plurality of transformations may be selected to suppress (reduceand/or eliminate) the transformation effects of the applied firstplurality of transformations in the spatial frequency domain. Forexample, if a linear phase shift is first applied in the spatialfrequency domain, a pixel shift may be applied thereafter in the imagedomain to mitigate the effects of the first transformation in thespatial frequency domain. Other examples of transformation pairsinclude: (1) a constant phase shift in the spatial frequency domain anda constant phase shift in the image domain; (2) a conjugation of data inthe spatial frequency domain and a reflection in the image domain; and(3) a rotation in the spatial frequency domain and a rotation in theimage domain.

In some embodiments, combining the plurality of transformed MR images toobtain the ensembled MR image comprises computing the ensembled MR imageas a weighted average of the plurality of transformed MR images. Forexample, the weight value of the weighted average may be determinedbased at least in part on the total number of varied model parametersand/or the total number of transformation functions applied to the inputMR data. Alternately, the weight value of the weighted average may bebased on which transformations are applied to the input MR data.

It may be desirable, in some embodiments, to remove the effects ofadjacent subject anatomy slices from a reconstructed image of a singlesubject anatomy slice. Accordingly, the inventors have developed methodsfor subtracting the contribution of a neighboring slice from a givenslice as a part of a self-ensembling technique. In some embodiments,where the input MR data comprises a first spatial frequency MR data(y_(i)) for generating an image for a first subject anatomy slice andsecond spatial frequency MR data (y_(i+1)) for generating an image for asecond subject anatomy slice, generating the plurality of transformedinput MR data instances comprises generating a first transformed inputMR data instance (y_(i) ⁺¹) by adding the second spatial frequency MRdata to the first spatial frequency MR data. Generating the plurality ofMR images comprises generating a first MR image (x_(i) ⁺¹) from thefirst transformed data instance (y_(i) ⁺¹) and generating a second MRimage (x_(i+1)) from the second MR spatial frequency data (y_(i+1)).Generating the ensembled MR image then comprises subtracting the secondMR image from the first MR image (x_(i) ⁺¹−x_(i+1)).

In some embodiments, the input MR data may comprise multiple MR datainstances, and it may be desirable to remove the effects of multipleadjacent subject anatomy slices from a reconstructed MR image of asingle subject anatomy slice. In such embodiments, the input MR data maycomprise first spatial frequency MR data for generating an image for afirst subject anatomy slice and second spatial frequency MR data forgenerating one or more images for one or more other subject anatomyslices. Generating the plurality of transformed input MR data instancesmay then comprise generating a first transformed input MR data instanceby combining the first spatial frequency MR data and the second spatialfrequency MR data. Additionally, generating the plurality of MR imagesmay comprise generating a first MR image from the first transformedinput MR data instance and generating one or more second MR images fromthe second spatial frequency MR data. Generating the ensembled MR imagemay then comprise subtracting the one or more second MR images from thefirst MR image.

FIG. 15 is a diagram 1500 illustrating a self-ensembling approach tonon-linear MR image reconstruction, in accordance with some embodimentsof the technology described herein. The self-ensembling technique may beexecuted by any suitable computing device. For example, in someembodiments, the self-ensembling technique may be performed by acomputing device co-located (e.g., in the same room) with an MRI systemthat obtained the MR data by imaging a subject (or object). As anotherexample, in some embodiments, the self-ensembling technique may beperformed by one or more processors located on the MRI system thatobtained the MR data. Alternately, in some embodiments, theself-ensembling technique may be performed by one or more processorslocated remotely from the MRI system (e.g., as part of a cloud computingenvironment) that obtained the input MR data.

The self-ensembling technique begins with an instance of input MR data1502, in some embodiments. The input MR data 1502 may be obtained by anMRI system (including any MRI systems as described herein) using anysuitable pulse sequence. Any suitable pre-processing may be performed toinput MR data 1502 prior to self-ensembling. The input MR data 1502 mayrepresent a single corresponding MR image in the image domain (e.g., theinput MR data 1502 may represent a single MR data gathering instance).In some embodiments, the input MR data 1502 may represent a singleanatomy slice of the imaged subject (or object).

The input MR data 1502 may be transformed by transformations T₁ . . .T_(N) to form transformed input MR data instances 1504-1 through 1504-N,in some embodiments. Transformations T₁ . . . T_(N) may be any suitabletransformation function configured to alter the input MR data 1502. Forexample, transformations T₁ . . . T_(N) may be any one of a non-limitinggroup of transformations, including linear phase shift transformations,constant phase shift transformations, complex conjugationtransformations, rotation transformations, transpose transformations,and/or reflection transformations. In some embodiments, thetransformations T₁ . . . T_(N) may include the identity transformation.Alternatively, an instance of the input MR data 1502 may be preserved(e.g., no transformation may be applied to the 0^(th) instance of inputMR data 1502 prior to MR image reconstruction).

In some embodiments, the transformed input MR data instances 1504-1through 1504-N may be reconstructed to form a plurality of MR images1508-0 through 1508-N. The MR image reconstruction may be performed by anon-linear MR image reconstruction process 1506, represented by:

x=f(y)

where y is the MR data in the spatial frequency domain, f(.) is thenon-linear reconstruction function, and x is the reconstructed MR imagein the image domain.

The non-linear MR image reconstruction process 1506 may be any suitablenon-linear MR image reconstruction technique. In some embodiments, thenon-linear MR image reconstruction process 1506 may be a neural networkmodel configured to perform MR image reconstruction. For example, theneural network model may be reconstruction neural network 212, asdescribed in connection with FIGS. 2A and 2C. Alternatively, in someembodiments, the non-linear MR image reconstruction process 1506 may beany suitable CS technique, examples of which are described herein.

In some embodiments, reverse transformations T₁ ⁻¹ . . . T_(N) ⁻¹ may beapplied to the plurality of MR images 1508-0 through 1508-N to formtransformed MR images 1508-0 through 1508-N. In some embodiments, thereverse transformations may include the identity transformation, whichmay be applied to MR image 1508-0. Alternatively, MR image 1508-0 may bepreserved (e.g., no reverse transformation may be applied to MR image1508-0 prior to ensembling).

It is to be appreciated that because a non-linear MR reconstructiontechnique is employed between the transformations T₁ . . . T_(N)performed in the spatial frequency domain and the reversetransformations T₁ ⁻¹ . . . T_(N) ⁻¹ performed in the imaging domain,that the reverse transformations T₁ ⁻¹ . . . T_(N) ⁻¹ are not, strictly,inverse transformations of transformations T₁ . . . T_(N). Rather,reverse transformations T₁ ⁻¹ . . . T_(N) ⁻¹ are selected to at leastpartially reverse and/or mitigate the effects of transformations T₁ . .. T_(N) in the image domain. For example, if a linear phase shift isfirst applied in the spatial frequency domain, a pixel shift may beapplied thereafter in the image domain to mitigate the effects of thefirst transformation in the spatial frequency domain. Other examples oftransformation pairs include: (1) a constant phase shift in the spatialfrequency domain and a constant phase shift in the image domain; (2) aconjugation of data in the spatial frequency domain and a reflection inthe image domain; and (3) a rotation in the spatial frequency domain anda rotation in the image domain.

After obtaining a transformed MR images 1508-0 through 1508-N, anensembled MR image 1512 may be formed, in some embodiments. Theensembled MR image 1512 may be represented mathematically as:

x _(self-ensemble)=Σ_(i) ^(N) w _(i) T _(i) ⁻¹ f(T _(i) y)

where N is the total number of transformation functions T_(i), and w_(i)is the weight for the given reconstruction. In some embodiments, theweight w_(i) may be based on the total number of transformationfunctions (e.g., w_(i)=1/N). Alternatively, the weight w_(i) may bebased on the particular transformation functions applied.

When the non-linear MR image reconstruction process 1506 is performed byusing a neural network model, additional parameters, θ, may be varied,such that the MR image reconstruction may be mathematically describedby:

x=f(y|θ)

and the ensembled MR image 1512 may be represented mathematically

x _(self-ensemble)=Σ_(j) ^(M)Σ_(i) ^(N) w _(ij) T _(i) ⁻¹ f(T _(i) y|θ_(j))

where M is the total number of varied model parameters, θ, and w_(ij) isthe weight for the given reconstruction. In some embodiments, the weightw_(i) may be based on the total number of transformation functions andthe total number of varied model parameters (e.g., w_(ij)=1/NM).Alternatively, the weight w_(ij) may be based on the particulartransformation functions applied.

In some embodiments, it may be desirable to reduce or eliminate noiseintroduced into an MR image of a particular subject anatomy slice by oneor more neighboring subject anatomy slices. Such noise contributions maybe addressed within the context of self-ensembling, as described herein,by using a “Mix-Up” technique and introducing the followingtransformation function to a given first input MR data, y_(i):

y _(i) ⁺¹ =T(y _(i))=y _(i) +y _(i+1)

where y_(i+1) is a subject anatomy slice proximate to slice y_(i).

The non-linear MR image reconstruction process 1506 may then bemathematically described as, for any non-linear reconstruction f(y):

x _(i) ⁺¹ =f(y _(i) ⁺¹),x _(i+1) =f(y _(i+1))

or, for a neural network model with additional parameters, θ:

x _(i) ⁺¹ =f(y _(i) ⁺¹|θ),x _(i+1) =f(y _(i+1)|θ)

After MR image reconstruction, reverse transformations may be applied tothe reconstructed MR images to subtract the contribution of the one ormore adjacent subject anatomy slices:

x _(i) ¹ =T ⁻¹(x _(i) ⁺¹)=x _(i) ⁺¹ −x _(i+1)

In some embodiments, one may generate many images, x_(i) ¹, using anysuitable number of adjacent subject anatomy slices (e.g., slices y_(i+1). . . y_(i+n)), which may be added to slice y_(i) as a part of transformT(y_(i)). In such embodiments, the final ensembled image may be obtainedby:

x _(self-ensemble)=Σ_(j) ^(N) x _(i) ^(j).

FIG. 16 is a flowchart of an illustrative process 1600 for performingnon-linear MR image reconstruction using self ensembling, in accordancewith some embodiments of the technology described herein. Process 1600may be executed using any suitable computing device. For example, insome embodiments, the process 1600 may be performed by a computingdevice co-located (e.g., in the same room) with an MRI system thatobtained the MR data by imaging a subject (or object). As anotherexample, in some embodiments, the process 1600 may be performed by oneor more processors located on the MRI system that obtained the MR data.Alternately, in some embodiments, the process 1600 may be performed byone or more processors located remotely from the MRI system (e.g., aspart of a cloud computing environment) that obtained the input MR data.

Process 1600 begins at act 1602, where input MR data in obtained. Insome embodiments, the input MR data had been previously obtained by anMRI system and stored for subsequent analysis, so that it is accessed atact 1602. In other embodiments, the input MR data may be obtained by anMRI system (including any of the MRI systems described herein) as partof process 1600.

In some embodiments, one or more pre-processing steps may be performedprior to moving to act 1604, where a plurality of transformed input MRdata is generated by applying a respective first plurality oftransformations to the input data. The transformations of the respectivefirst plurality of transformations may be any suitable transformationsin the spatial frequency domain configured to alter the input MR data.For example, the transformations of the respective first plurality oftransformations may be the transformations T₁ . . . T_(N) as describedin connection with FIG. 15 herein.

After act 1604, the process 1600 may move to act 1606, where a pluralityof MR images may be generated from the plurality of transformed input MRdata instances and the input MR data using a non-linear MR imagereconstruction technique. The non-linear MR image reconstructiontechnique used to generate the plurality of MR images may be anysuitable non-linear MR image reconstruction technique, as describedherein. In some embodiments, the non-linear MR image reconstructionprocess 1506 may be a neural network model configured to perform MRimage reconstruction. For example, the neural network model may bereconstruction neural network 212, as described in connection with FIGS.2A and 2C. Alternatively, in some embodiments, the non-linear MR imagereconstruction process 1506 may be any suitable CS technique, asdescribed herein.

After act 1606, the process 1600 may move to act 1608, where anensembled MR image may be generated from the plurality of MR images, insome embodiments. The ensembled MR image may be generated at least inpart by applying a second plurality of transformations to the pluralityof MR images to obtain a plurality of transformed images. The secondplurality of transformations may include any suitable transformations toreverse and/or mitigate the effects of the first plurality oftransformations in the image domain, as described herein. The ensembledMR image may also be generated at least in part by combining theplurality of transformed MR images to obtain the ensembled MR image, insome embodiments. Combining the plurality of transformed MR images toobtain the ensembled MR image may comprise, for example, performing anaverage or a weighted average (e.g., adding images weighted by positiveand/or negative weights), as described herein.

After act 1608, the process 1600 may move to act 1610, where theensembled MR image may be output. The ensembled MR image may be outputusing any suitable method. For example, the ensembled MR image may beoutput by being saved for subsequent access, transmitted to a recipientover a network, and/or displayed to a user of the MRI system.

FIGS. 17A and 17B show example MR images of a subject's brain obtainedwithout self-ensembling and with self-ensembling, respectively. TheMix-Up self-ensembling technique is used to produce FIG. 17B, whichresults in an MR image having sharper contrast as compared to the imagereconstruction of FIG. 17A obtained without self ensembling.

FIGS. 18A and 18B show example MR images of a subject's brain obtained(e.g., by different RF coils) without self-ensembling and withself-ensembling, respectively. The self-ensembling technique used toproduce FIG. 18B is performed using geometrical data augmentation. Insome such embodiments, the transformations used in self-ensembling mayinclude a complex conjugation transformation in the spatial frequencydomain and a reflection in the image domain. The example of FIG. 18Bemployed the following example transformations in the spatial frequencydomain:

-   -   T₀=identity function    -   T₁=complex conjugation

and the following transformations in the image domain:

-   -   T₀ ⁻¹=reverse identity function    -   T₁ ⁻¹=reflection

to perform the following self-ensembling:

x _(self-ensemble)=Σ_(i) ²0.5T _(i) ⁻¹ f(T _(i) y|θ).

FIGS. 19A and 19B show example MR images of a subject's brain obtainedwithout self-ensembling and with self-ensembling, respectively. Theself-ensembling technique used to produce FIG. 19B includes the Mix-Uptechnique and geometrical data augmentation, as described herein. As maybe observed from FIGS. 18A-B and 19A-B, self-ensembling produces sharperreconstructions having a higher contrast.

Coil Estimation

As described herein, in some embodiments, an MRI system may includemultiple RF coils configured to detect MR data while the MRI system isimaging a subject. In such embodiments, the MR data obtained from eachof the multiple RF coils may be combined to generate one or more imagesof the subject.

For example, in some embodiments, multiple MR images may be generatedfrom spatial frequency data collected by a respective plurality of RFcoils, and the multiple MR images may be combined to generate a singleimage of the subject. This is sometimes termed “parallel imaging”. Forexample, starting with N_(coil) MR images: x₁, . . . , x_(N) _(coil) ,these images may be combined using the following weighted combination,for each pixel location r in the image x(r):

$x = {\sum\limits_{i = 1}^{N_{coil}}\frac{s_{i}^{*}x_{i}}{\sum\limits_{j = 1}^{N_{coil}}{S_{j}^{*}S_{j}}}}$

where (.)* denotes complex conjugation, where S_(j) represents theprofile of the jth RF coil, and where the index r is suppressed forclarity. The coil profile S_(j) for the jth RF coil may indicate thesensitivity of the jth coil to MR signals at various locations in thefield of view. For this reason, a coil profile may sometimes be termed acoil sensitivity profile. In some embodiments, a coil profile may bespecified at a per-pixel or per-voxel level, each entry indicative ofthe sensitivity of a coil to MR signals emitted from that pixel orvoxel. The sensitivity of a coil may be a higher for a pixel/voxelcloser to the coil than for a pixel/voxel in a region far from the coil.

In situations where the noise correlation L is known (e.g., is anN_(coil)×N_(coil) matrix), the individual images, one per coil, may becombined according to the following equation in matrix form (againpixel-wise for each r):

x=(Ŝ ^(H) L ⁻¹ Ŝ)⁻¹ Ŝ ^(H) L ⁻¹ {circumflex over (x)}

where {circumflex over (x)}=[x₁, . . . , x_(N) _(coil) ], Ŝ=[S₁, . . . ,S_(N) _(coil) ] for each pixel location.

Parallel imaging is a popular reconstruction technique because theresulting combined image has a higher signal-to-noise ratio than theconstituent RF coil images. When the RF coil profiles are known inadvance, then the combination equations described above are optimalestimates of the combined image in a least-squares sense (or in themaximum likelihood sense under a Gaussian noise assumption). The aboveequations can be used when the RF coil profiles are known. When the RFcoil profiles are not known, not the images may be computed according toa residual sum of squares (RSS) technique, but this results in alower-quality and lower-SNR image.

Accordingly, in some embodiments, the inventors have developed a neuralnetwork model (e.g., the neural network model shown in FIG. 20B) forestimating the sensitivity profile of an RF coil from data collected bythe RF coil. The sensitivity profiles estimated by the neural networkmay be used to combine images obtained during parallel imaging withmultiple RF coils to obtain combined images of a subject. The resultingneural-network based parallel imaging technique developed by theinventors outperforms both conventional parallel imaging based onresidual sum of squares estimates of coil sensitivity and the adaptivereconstruction technique described in D. O. Walsh, A. F. Gmitro, and M.W. Marcellin, “Adaptive Reconstruction of Phased Array MR Imagery,”Magnetic Resonance in Medicine 42:682-690 (2000).

Accordingly, some embodiments provide for a method for generatingmagnetic resonance (MR) images from MR data obtained by an MRI systemcomprising a plurality of RF coils (e.g., 8, 16, 32, etc.) configured todetect RF signals. The method includes: (A) obtaining a plurality ofinput MR datasets (e.g., 8, 16, 32, etc.) obtained by the MRI systemwhile imaging a subject, each of the plurality of input MR datasetscomprising spatial frequency data and obtained using a respective RFcoil in the plurality of RF coils; (B) generating a respective pluralityof MR images from the plurality of input MR datasets by using an MRimage reconstruction technique (e.g., using a neural network, compressedsensing, a non-uniform Fourier transformation, a Fourier transformation,etc.); (C) estimating, using a neural network model, a plurality of RFcoil profiles corresponding to the plurality of RF coils; (D) generatingan MR image of the subject using the plurality of MR images and theplurality of RF coil profiles; and (E) outputting the generated MRimage.

In some embodiments, generating the MR image of the subject using theplurality of MR images and the plurality of RF coil profiles comprisesgenerating the MR image of the subject as a weighted combination of theplurality of MR images, each of the plurality of MR images beingweighted by a respective RF coil profile in the plurality of RF coilprofiles. In some embodiments, the plurality of MR images comprises afirst MR image generated from a first input MR dataset obtained using afirst RF coil of the plurality of RF coils, and wherein generating theMR image of the subject comprises weighting different pixels of thefirst MR image using different values of a first RF coil profile amongthe plurality of RF coil profiles, the first RF coil profile beingassociated with the first RF coil.

In some embodiments, the neural network may be a convolutional neuralnetwork. The neural network may be a 2D or a 3D convolutional neuralnetwork. The neural network may include one or more convolutionallayers, one or more non-linearity layers (e.g., rectified linear unitlayers), and/or one or more fully connected layers. In some embodiments,the neural network's input may be (e.g., complex-valued) input obtainedfrom MR measurements detected by an RF coil (e.g., not just themagnitude of the reconstructed image, but both the magnitude and thephase) and the output may be the sensitivity profile for the RF coil.

An illustrative example of a neural network architecture that may beused for estimating coil profiles, in some embodiments, is shown in FIG.20B. This is a 2D convolutional neural network having the followinglayers and associated parameters:

Layer 1: 2D convolution, kernel size=3×3, stride=1, 64 features, ReLU

Layer 2: 2D convolution, kernel size=3×3, stride=1, 64 features, ReLU

Layer 3: 2D convolution, kernel size=3×3, stride=2, 64 features, ReLU

Layer 4: 2D convolution, kernel size=3×3, stride=1, 128 features, ReLU

Layer 5: 2D convolution, kernel size=3×3, stride=1, 128 features, ReLU

Layer 6: 2D convolution, kernel size=3×3, stride=2, 128 features, ReLU

Layer 7: 2D convolution, kernel size=3×3, stride=1, 256 features, ReLU

Layer 8: 2D convolution, kernel size=3×3, stride=1, 256 features, ReLU

Layer 9: 2D convolution, kernel size=3×3, stride=1, 256 features, ReLU

Layer 10: 2D transposed convolution, kernel size=4×4, stride=2, 64features, ReLU

Concatenate output from Layer 6 and Layer 10

Layer 12: 2D convolution, kernel size=3×3, stride=1, 64 features, ReLU

Layer 13: 2D convolution, kernel size=3×3, stride=1, 64 features, ReLU

Layer 14: 2D transposed convolution, kernel size=4×4, stride=2, 64features, ReLU

Layer 15: 2D convolution, kernel size=3×3, stride=1, 64 features, ReLU

Layer 16: 2D convolution, kernel size=3×3, stride=1, 64 features, ReLU

Layer 17: 2D convolution, kernel size=3×3, stride=1, 64 features, Tan h

A neural network, like the network of FIG. 20B, for estimating coilprofiles may be trained in any of numerous ways. In some embodiments,training the neural network may comprise generating training data bysimulating complex phase for various MR images and training the neuralnetwork to predict the coil profile from complex-valued image data. Insome embodiments, the neural network may take as input individual coilreconstructions x_(rec-i) and produce the corresponding estimated coilprofile S_(rec-i)=f_(cnn)(x_(rec-i)|θ), or take all N_(coil) input andproduce N_(coil) sensitivity profiles jointly. Given the dataset

that contains the coil weighted images x₁, . . . , x_(N) _(coil) and theground truth sensitivity maps S₁, . . . S_(N) _(coil) , the network canbe trained using the following loss function:

${\mathcal{L}(\theta)} = {\sum\limits_{j = 1}^{}{\sum\limits_{i = 1}^{N_{coil}}{{S_{i}^{(j)} - S_{{rec} - i}^{(j)}}}_{2}}}$

Alternatively, in some embodiments, a neural network may be trained todirectly obtain a coil combination. Let f_(cnn)(.|θ) express aconvolutional neural network, where the input to the network is N_(coil)reconstructed images x_(rec-1), . . . , x_(rec-N) _(coil) . The networkoutput is a complex-valued combined image x_(combined). In such asituation, the loss function can be expressed as:

${\mathcal{L}(\theta)} = {\sum\limits_{j = 1}^{|\; |}{{x^{(j)} - x_{ccombined}^{(j)}}}_{2}}$

In this alternative approach, the sensitivity profile is implicitlylearnt, and the network will perform optimal combination based on thedata.

In some embodiments, training data for training a neural network forestimating coil profiles may be generated synthetically from a datasetof existing MR scans. For example, in some embodiments, an MR image xmay be loaded from a dataset and random phase may be added to this imageto obtain a complex-valued image (since only magnitudes are typicallyavailable in existing datasets). Complex-valued coil profiles S_(i) forN_(coil) coils may be synthesized next. For example, the sensitivityvalues for particular pixels/voxels may be sampled according to aGaussian distribution and random phase may be added. Next, Gaussiannoise e_(i) may be added (potentially with a simulated noise correlationmatrix) to obtain simulated coil images x_(i) according to:

x _(i) =S _(i) x+e _(i) for i=1 . . . N _(coil).

The resulting images x_(i) may be transformed to the spatial frequencydomain and, optionally, undersampled to simulate the type of samplingtrajectories that might be expected to be used in practice. Thissimulation process may be repeated for any suitable number of imagesfrom the data set (of e.g., brain scans or any other type of MR scans).

FIG. 20A is a flowchart of an illustrative process 2000 for generatingan MR image from input MR spatial frequency data collected by multipleRF coils, in accordance with some embodiments of the technologydescribed herein. Process 2000 may be performed by any suitablecomputing device(s). For example, process 2000 may be performed by oneor more processors (e.g., central processing units and/or graphicsprocessing units) part of the MRI system and/or by one or moreprocessors external to the MRI system (e.g., computers in an adjoiningroom, computers elsewhere in a medical facility, and/or on the cloud).

Process 2000 begins at act 2002, where a plurality of input MR datasetspreviously obtained by an MRI system are accessed. The MRI systemincludes multiple RF coils (say “N” coils, without loss of generality),and each of the plurality of input MR data sets includes data collectedby a respective RF coil from among the multiple RF coils.

Next, process 2000 proceeds to act 2004, where a plurality of MR imagesare generated from the plurality of input datasets obtained at act 2002using an MR image reconstruction technique. Any suitable MR imagereconstruction technique may be used. For example, the reconstructionmay be performed using any neural network reconstruction techniquedescribed herein (e.g., using neural network 212). As another example,the reconstruction may be performed using compressed sensing and/or anyother suitable type of non-linear reconstruction technique. As yetanother example, the reconstruction may be performed using a uniform ora non-uniform Fourier transformation. The plurality of MR images mayinclude both magnitude and phase information (they may becomplex-valued).

Next, at act 2006, estimates of the plurality of RF coil profiles aregenerated by providing the plurality of MR images as input to a neuralnetwork model. In some embodiments, the estimates of the RF coilprofiles may be generated jointly—the plurality of MR images generatedat act 2004 are simultaneously provided as input to the neural networkmodel. In other embodiments, the estimates of the RF coil profiles maybe generated separately—a profile for a particular RF coil may begenerated by applying a neural network to an image generated from datacollected by the particular RF coil. Examples of neural network modelsthat may be applied at act 2006 are described herein including withreference to FIG. 20B. In some embodiments, the output of the neuralnetwork may be smoothed (e.g., using a median or Gaussian filter) priorto being used at act 2008.

Next, at act 2008, the plurality of MR images are combined to generatean image of the subject using the RF coil profiles generated at act2006. This may be done in any suitable way. For example, the combinedimage of the subject may be generated as a weighted combination of theplurality of MR images, each of the plurality of MR images beingweighted by a respective RF coil profile in the plurality of RF coilprofiles. The weighting may be computed according to:

$x = {\sum\limits_{i = 1}^{N_{coil}}\frac{S_{i}^{*}x_{i}}{\sum\limits_{j = 1}^{N_{coil}}{S_{j}^{*}S_{j}}}}$

where the RF coil profiles S_(j) are estimated using the neural networkat act 2006 of process 2000.

After the combined image is computed at act 2008, the combined image isoutput at act 2010 (e.g., to a screen, saved to a memory, sent toanother computing device, etc.).

FIGS. 20C-20H illustrate performance of the neural network coil profileestimation techniques described herein. FIGS. 20C and 20D showreconstructions a phantom imaged using multiple RF coils usingconventional the residual sum of squares and adaptive approaches (of D.O. Walsh, A. F. Gmitro, and M. W. Marcellin). FIGS. 20E and 20F showresults obtained using the neural network techniques described herein.Both FIGS. 20E and 20F show results obtained by estimating individual RFcoil profiles using the neural network of FIG. 20B, with the results ofFIG. 20F differing only in that the output of the neural network wassmoothed prior to the combination of the images. The higher SNR andquality of the resulting images in FIGS. 20E and 20F (as compared to theresults shown in FIGS. 20C and 20D) are readily apparent.

FIG. 20G (top) shows images of a patient's brain obtained using parallelimaging and the conventional residual sum of squares technique, whichare of lower quality and have lower SNR than the images shown in thebottom half of FIG. 20G, which were obtained using the neural networktechniques described herein.

FIG. 20H (top) shows images of another patient's brain obtained usingparallel imaging and the conventional residual sum of squares technique,which are of lower quality and have lower SNR than the images shown inthe bottom half of FIG. 20H, which were obtained using the neuralnetwork techniques described herein.

Coil Compression

In some of the embodiments in which multiple RF coils are used tocollect MR data in parallel (parallel imaging), the data may betransformed as though it were observed by a smaller number of virtual RFcoils, with the data “observed” by the virtual RF coils being derivedfrom the data actually observed by the physical RF coils part of the MRIsystem.

For example, in some embodiments, if the MRI system collects data using16 RF coils, the collected data may be transformed using a lineartransformation A as though it were observed by 8 virtual RF coils. As aspecific non-limiting example, suppose each of the 16 RF coils were tocollect 100 measurements, then measurements may be organized in a 16×100matrix M of data. In turn, the linear transformation A may be a 8×16matrix, such that when it is applied to the data (by computing thematrix product AM), the resulting data for the virtual coils is an 8×100matrix of data in which at each of 100 time points, eight data pointscorresponding to eight virtual RF coils are to be used for furtherprocessing instead of 16 data points corresponding to 16 physical RFcoils.

There are numerous benefits to performing such a transformation, whichis sometimes termed “geometric coil compression.” Generally, one benefitis that geometric coil compression will transform the data so that thesignals from the dominant RF coils are emphasized in subsequentprocessing. Moreover, the inventors have recognized that geometric coilcompression has particular benefits when used in conjunction with theneural network techniques described herein. First, using coilcompression to reduce the input data to a fixed number of virtual RFcoils allows the neural networks described herein to be trainedindependently of the number of physical RF coils in the MRI system inwhich the neural networks will be deployed. In this way, neural networkstrained for processing data from M virtual RF coils may be deployed inany MRI system that has M or more physical RF coils. This also providesflexibility if one or more RF coils in an MRI system is taken offline.

Second, RF coil compression allows for improved training of neuralnetworks because each of the virtual RF channels contains moreinformation than the physical RF channels would have, which makes iteasier for the neural network training algorithms to extract informationfor estimating neural network rates, resulting in faster training (e.g.,fewer iterations thereby reducing computational resources required fortraining) and improved performance. Reducing the number of channels alsoreduces the overall number of parameters to be estimated in the neuralnetwork models described herein, which also improves trainingperformance.

Accordingly, in some embodiments, the neural network models describedherein may be trained to process data that has been coil compressed. Inthis way, when a neural network (e.g., the reconstruction neural network212 or any other neural network described herein) is deployed to processMR data collected by multiple RF coils, the collected data is first coilcompressed (e.g., by a suitable transformation A) and then provided tothe neural network.

In some embodiments, the linear transformation A (sometimes termed thecoil compression matrix) may be found as follows. Let three-dimensional(3D) k-space be indexed by each location k=[k_(x), k_(y), k_(z)]^(T),and let a multi-coil k-space value be given by v(k)=[v₁(k), v₂(k) . . ., v_(N) _(coil) (k)], where N_(coil) represents the number of physicalRF coils in an MRI system (e.g., 4, 8, 16, 32, 64, 128, any number ofcoils between 16 and 64, any number of coils between 32 and 128, or anyother suitable number or range within these ranges). Let the coilcompression matrix be a complex-valued M×N_(coil) matrix A∈

^(M×N) ^(coil) such that v′=Av, and v is the corresponding k-space datarepresented as M virtual coils. In some embodiments, the coilcompression matrix A may be determined according to:

min._(A)∥(A ^(H) A−I)v(k)∥² s.t.AA ^(H) =I.

In some embodiments, the process of 2000 generating an MR image frominput MR spatial frequency data collected by multiple coils may beadapted to utilize the geometric coil compression techniques describedherein. An illustrative example is described next with reference to FIG.21, which is a flowchart of an illustrative process 2100 for generatingan MR image using geometric coil compression from data obtained bymultiple physical RF coils, in accordance with some embodiments of thetechnology described herein. Process 2100 may be performed by anysuitable computing device(s). For example, process 2100 may be performedby one or more processors (e.g., central processing units and/orgraphics processing units) part of the MRI system and/or by one or moreprocessors external to the MRI system (e.g., computers in an adjoiningroom, computers elsewhere in a medical facility, and/or on the cloud).

Process 2100 begins at act 2102, where a plurality of input MR datasetspreviously obtained by an MRI system are accessed. The MRI systemincludes multiple RF coils (say “N” coils, without loss of generality),and each of the plurality of input MR data sets includes data collectedby a respective RF coil from among the multiple RF coils.

Next, process 2100 proceeds to act 2104, where geometric coilcompression is performed on the data accessed at act 2102. Applyinggeometric coil compression to the plurality of input MR datasetsgenerates a respective plurality of virtual input data sets. In someembodiments, generating the virtual input data sets involves: (1)determining the coil compression matrix A; and (2) applying the coilcompression matrix A to the plurality of input MR data sets to obtainedthe respective plurality of virtual input MR datasets. In someembodiments, determining the coil compression matrix A may involvedetermining the coil compression matrix from the data in the pluralityof input MR datasets. The determining may be performed using anoptimization such as, for example, (min._(A)∥(A^(H)A−I)v(k)∥² s.t.AA^(H)=I.

In some embodiments, the geometric coil compression may reduce thenumber of channels by a factor of 2 (e.g., from 16 physical RF coils to8 virtual RF coils or fewer, from 32 physical RF coils to 16 virtual RFcoils or fewer, etc.), by a factor of 4 (e.g., from 32 physical RF coilsto 8 virtual RF coils or fewer), or by any other suitable factor, asaspects of the technology described herein are not limited in thisrespect.

Next, process 2100 proceeds to act 2106, where a plurality of MR imagesis generated from the plurality of virtual input MR data. This may beperformed using any suitable reconstruction technique. For example, thereconstruction may be performed using any neural network reconstructiontechnique described herein (e.g., using neural network 212). As anotherexample, the reconstruction may be performed using compressed sensingand/or any other suitable type of non-linear reconstruction technique.As yet another example, the reconstruction may be performed using auniform or a non-uniform Fourier transformation.

Next, at act 2108, the plurality of MR images are combined to generatean image of the subject. This may be done in any suitable way includingin any of the ways described with respect to act 2008 of process 2000.The generated image is then output at act 2110.

Pre-Whitening

The inventors have appreciated that, when MR data are being collected inparallel by multiple RF coils (“parallel imaging”), different RF coilsmay detect different amounts and/or types of noise. As a result, thereceived noise may be unevenly distributed among the multiple receivechannels. For example, even if the noise were uncorrelated and uniformlydistributed among k-space locations, there may nonetheless be noiselevel differences between the individual RF coils, and the noisedetected by one RF coil may be correlated with the noise detected byanother RF coil. Left uncorrected, such level differences andcorrelations may lead to a reduction of image quality and SNR.

Accordingly, in some embodiments, the relationship of noise signalsreceived by multiple receive coils may be represented by an N×N matrix,where N is the number of coils, expressed as Ψ_(ij)=

η_(i), η_(j) ^(H)

, where η_(i) is the noise component of the i^(th) signal. This matrixwill not be the identity matrix due to correlation among the noisesignals received using different RF coils and/or relatively differentamounts of noise observed by the different RF coils. In someembodiments, specific values of such a matrix may be obtained during acalibration stage when the RF coils measure noise levels without asubject being imaged so that no MR signal is present. Any suitablecorrelation estimation technique may be used in this regard, as aspectsof the technology described herein are not limited in this respect.

Accordingly, given the matrix Ψ_(ij), in some embodiments, apre-whitening matrix W may be estimated from the matrix Ψ_(ij) andsubsequently applied to the input data prior to the data being processedby the neural network algorithms described herein. In particular, someembodiments involve determining the pre-whitening matrix W such thatv_(pw)=Wv, where v is the original k-space measurement, v_(pw) is theprewhitened k-space measurement, and so that W satisfies W^(T)W=Ψ⁻¹.Applying W to the input data allows for the received signals to bedecorrelated, which in turn improves the quality and SNR of the imagesobtained from these data.

The pre-whitening matrix W may be estimated in any suitable way. Forexample, in some embodiments, W may be determined using zero-phasecomponent analysis (ZCA) according to: W=Ψ^(−1/2). As another example,in some embodiments, Wmay be determined using principal componentsanalysis (PCA) according to: W=Γ⁻¹U^(T), where Ψ=UΓ^(−1/2)U^(T) is thesingular value decomposition (SVD) of Ψ. As yet another example, in someembodiments, W may be determined used the Cholesky decompositionaccording to: W=L⁻¹, where LL^(H)=Ψ is the Cholesky decomposition.

k-Space Weighting

The inventors have appreciated that the neural network techniquesdescribed herein may be improved if the input MR spatial frequency datawere weighted in the spatial frequency domain (k-space). In particular,the inventors have appreciated that weighting input MR spatial frequencydata in k-space prior to reconstruction may improve the quality of thereconstruction. Accordingly, in some embodiments, the input MR spatialfrequency data may be weighted in k-space prior to or as part ofreconstruction.

In some embodiments, the input MR spatial frequency data may be weightedby using a weighting function known in advance. For example, individualinput MR spatial frequency data points may be weighted based on theirdistances to the k-space origin (e.g., points closer to the origin ofk-space are given greater weight or points closer to the origin ofk-space are given less weight). As another example, input MR spatialfrequency data may be weighted using a weighting function based on thewavelet transform given by:

${\psi_{s}(w)} = {\frac{1}{\sqrt{2^{s}}}\frac{i\; 2^{s}w}{2}\left( \frac{{\sin \left( {2^{s}w} \right)}/4}{2^{s}{w/4}} \right)^{2}{\exp \left( {{- i}\frac{2^{s}w}{2}} \right)}}$

where w is a frequency, which can be |k| for n-dimensional k-space data,and s is a scale, which may be determined based on the image resolution,k-space grid size, and/or the degree to which the data is undersampledin k-space.

Additionally or alternatively, the k-space weighting may be learned. Insome embodiments, for example, the neural network (e.g., reconstructionneural network 212) may include a layer for weighting the input datanon-uniformly in the spatial frequency domain. The weights of thisneural network layer may be learned during training, and the lossfunction used for training the neural network may include one or moreterms to guide the type of weighting that is to be learned (e.g., toweight more near the k-space origin, away from the k-space origin, neara particular region of k-space, or in any other suitable way). In thisway, the weighting may not only be learned (resulting in improvedperformance relative to known weightings that are fixed in advance), butalso may be learned jointly with other parameters of the neural networksdescribed herein, further improving overall reconstruction performance.

Example MRI Systems

Some embodiments of the technology described herein may be implementedusing portable low-field MRI systems, aspects of which are describedbelow with reference to FIGS. 22, 23, 24A-B, and 25A-B. Some aspects ofsuch portable low-field MRI systems are further described in U.S. Pat.No. 10,222,434, filed on Jan. 24, 2018, titled “Portable MagneticResonance Imaging Methods and Apparatus,” which is incorporated byreference in its entirety herein.

FIG. 22 is a block diagram of example components of a MRI system 2200.In the illustrative example of FIG. 22, MRI system 2200 comprisesworkstation 2204, controller 2206, pulse sequences store 2208, powermanagement system 2210, and magnetic components 2220. It should beappreciated that system 2200 is illustrative and that an MRI system mayhave one or more other components of any suitable type in addition to orinstead of the components illustrated in FIG. 22.

As illustrated in FIG. 22, magnetic components 2220 comprise B₀ magnet2222, shims 2224, RF transmit and receive coils 2226, and gradient coils2228. B₀ magnet 2222 may be used to generate, at least in part, the mainmagnetic field B₀. B₀ magnet 2222 may be any suitable type of magnetthat can generate a main magnetic field, and may include one or more B₀coils, correction coils, pole pieces, etc. In some embodiments, B₀magnet 2222 may be a permanent magnet. For example, in some embodiments,B₀ magnet 222 may comprise multiple permanent magnet pieces organized ina bi-planar arrangement of concentric permanent magnet rings asdescribed herein including with reference to FIG. 23. In someembodiments, B₀ magnet 2222 may be an electromagnet. In someembodiments, In some embodiments, B₀ magnet 2222 may be a hybrid magnetcomprising one or more permanent magnets and one or more electromagnets.

In some embodiments, shims 2224 may be used to contribute magneticfield(s) to improve the homogeneity of the B₀ field generated by magnet2222. In some embodiments, shims 2224 may be permanent magnet shims. Insome embodiments, shims 2224 may be electromagnetic and may comprise oneor more shim coils configured to generate a shimming magnetic field. Insome embodiments, gradient coils 2228 may be arranged to providegradient fields and, for example, may be arranged to generate gradientsin the magnetic field in three substantially orthogonal directions (X,Y, Z) to localize where MR signals are induced. In some embodiments, oneor more magnetics components 2220 (e.g., shims 2224 and/or gradientcoils 2228) may be fabricated using the laminate techniques.

In some embodiments, RF transmit and receive coils 2226 may comprise oneor multiple transmit coils that may be used to generate RF pulses toinduce a magnetic field B₁. The transmit/receive coil(s) may beconfigured to generate any suitable type of RF pulses configured toexcite an MR response in a subject and detect the resulting MR signalsemitted. RF transmit and receive coils 2226 may include one or multipletransmit coils and one or multiple receive coils. The configuration ofthe transmit/receive coils varies with implementation and may include asingle coil for both transmitting and receiving, separate coils fortransmitting and receiving, multiple coils for transmitting and/orreceiving, or any combination to achieve single channel or parallel MRIsystems.

In some embodiments, RF transmit and receive coils 2226 include multipleRF coils, which allow the MRI system 2200 to concurrently receive MRsignals on multiple channels. In some embodiments, the MR signalsreceived by multiple RF coils may be processed and combined using thetechniques described herein including with reference to FIGS. 20 and 21.

Power management system 2210 includes electronics to provide operatingpower to one or more components of the low-field MRI system 2200. Forexample, power management system 2210 may include one or more powersupplies, gradient power amplifiers, transmit coil amplifiers, and/orany other suitable power electronics needed to provide suitableoperating power to energize and operate components of the low-field MRIsystem 2200.

As illustrated in FIG. 22, power management system 2210 comprises powersupply 2212, amplifier(s) 2214, transmit/receive switch 2216, andthermal management components 2218. Power supply 2212 includeselectronics to provide operating power to magnetic components 2220 ofthe low-field MRI system 2200. For example, in some embodiments, powersupply 2212 may include electronics to provide operating power to one ormore B₀ coils (e.g., B₀ magnet 2222 when it is an electromagnet) toproduce the main magnetic field for the low-field MRI system, one ormore shims 2224, and/or one or more gradient coils 1628. In someembodiments, power supply 2212 may be a unipolar, continuous wave (CW)power supply. Transmit/receive switch 2216 may be used to select whetherRF transmit coils or RF receive coils are being operated.

In some embodiments, amplifier(s) 2214 may include one or more RFreceive (Rx) pre-amplifiers that amplify MR signals detected by RFreceive coil(s) (e.g., coils 2224), RF transmit (Tx) amplifier(s)configured to provide power to RF transmit coil(s) (e.g., coils 2226),gradient power amplifier(s) configured to provide power to gradientcoil(s) (e.g., gradient coils 2228), and/or shim amplifier(s) configuredto provide power to shim coil(s) (e.g., shims 2224 in embodiments whereshims 2224 include one or more shim coils).

In some embodiments, thermal management components 2218 provide coolingfor components of low-field MRI system 2200 and may be configured to doso by facilitating the transfer of thermal energy generated by one ormore components of the low-field MRI system 2200 away from thosecomponents. Thermal management components 2218 may include components toperform water-based or air-based cooling, which may be integrated withor arranged in close proximity to MRI components that generate heatincluding, but not limited to, B₀ coils, gradient coils, shim coils,and/or transmit/receive coils.

As illustrated in FIG. 22, low-field MRI system 2200 includes controller2206 (also referred to as a console) having control electronics to sendinstructions to and receive information from power management system2210. Controller 2206 may be configured to implement one or more pulsesequences, which are used to determine the instructions sent to powermanagement system 2210 to operate the magnetic components 2220 accordingto a desired sequence. For example, controller 2206 may be configured tocontrol the power management system 2210 to operate the magneticcomponents 2220 in accordance with a balanced steady-state freeprecession (bSSFP) pulse sequence, a low-field gradient echo pulsesequence, a low-field spin echo pulse sequence, a low-field inversionrecovery pulse sequence, arterial spin labeling, diffusion weightedimaging (DWI), and/or any other suitable pulse sequence.

In some embodiments, controller 2206 may be configured to implement apulse sequence by obtaining information about the pulse sequence frompulse sequences repository 2208, which stores information for each ofone or more pulse sequences. Information stored by pulse sequencesrepository 2208 for a particular pulse sequence may be any suitableinformation that allows controller 2206 to implement the particularpulse sequence. For example, information stored in pulse sequencesrepository 2208 for a pulse sequence may include one or more parametersfor operating magnetics components 2220 in accordance with the pulsesequence (e.g., parameters for operating the RF transmit and receivecoils 2226, parameters for operating gradient coils 2228, etc.), one ormore parameters for operating power management system 2210 in accordancewith the pulse sequence, one or more programs comprising instructionsthat, when executed by controller 2206, cause controller 2206 to controlsystem 2200 to operate in accordance with the pulse sequence, and/or anyother suitable information. Information stored in pulse sequencesrepository 2208 may be stored on one or more non-transitory storagemedia.

As illustrated in FIG. 22, in some embodiments, controller 2206 mayinteract with computing device 2204 programmed to process received MRdata (which, in some embodiments, may be spatial frequency domain MRdata). For example, computing device 2204 may process received MR datato generate one or more MR images using any suitable imagereconstruction process(es) including using any of the techniquesdescribed herein that make use of neural network models to generate MRimages from spatial frequency MR data. For example, computing device2204 may perform any of the processes described herein with reference toFIGS. 2D, 2D, 8A-8B, 16, 20, and 21. Controller 2206 may provideinformation about one or more pulse sequences to computing device 2204for the processing of data by the computing device. For example,controller 2206 may provide information about one or more pulsesequences to computing device 2204 and the computing device may performan image reconstruction process based, at least in part, on the providedinformation.

In some embodiments, computing device 2204 may be any electronicdevice(s) configured to process acquired MR data and generate image(s)of the subject being imaged. However, the inventors have appreciatedthat it would be advantageous for a portable MRI system to havesufficient onboard computing capability to perform neural networkcomputations to generate MR images from input spatial frequency databecause in many settings (e.g., hospitals), there is limited networkbandwidth available for offloading spatial frequency MR data from theMRI machine for processing elsewhere (e.g., in the cloud). Accordingly,in some environments where the MRI system 2200 may be deployed, theinventors have recognized that it is advantageous for the MRI system toinclude hardware specialized for neural network calculations to performsome of the processes described herein.

Accordingly, in some embodiments, computing device 2204 may include oneor multiple graphics processing units (GPU) configured to perform neuralnetwork calculations that are to be performed when the neural networkmodels described herein (e.g., neural network model 204,pre-reconstruction neural network 210, reconstruction neural network212, post reconstruction neural network 214, any of their constituentneural networks, and/or any other neural networks). In some suchembodiments, computing device 2204 may be onboard (e.g., within thehousing of the low-field MRI system 2200). Accordingly, in someembodiments, MRI system 2200 may include one or more GPU(s) and theGPU(s) may be onboard, for example by being housed within the samehousing as one or more components of the power components 2210.Additionally or alternatively, computing device 2204 may include one ormore hardware processors, FPGAs, and/or ASICs configured to processacquire MR data and generate image(s) of the subject being imaged.

In some embodiments, a user 2202 may interact with computing device 2204to control aspects of the low-field MR system 2200 (e.g., program thesystem 2200 to operate in accordance with a particular pulse sequence,adjust one or more parameters of the system 2200, etc.) and/or viewimages obtained by the low-field MR system 2200.

FIG. 23 illustrates bi-planar permanent magnet configurations for a B₀magnet, in accordance with some embodiments of the technology describedherein. FIG. 23 illustrates a permanent B₀ magnet 2300 formed bypermanent magnets 2310 a and 2310 b arranged in a bi-planar geometry anda yoke 2320 that captures electromagnetic flux produced by the permanentmagnets and transfers the flux to the opposing permanent magnet toincrease the flux density between permanent magnets 2310 a and 2310 b.Each of permanent magnets 2310 a and 2310 b is formed from a pluralityof concentric permanent magnet rings. As shown in FIG. 23, permanentmagnet 2310 b comprises an outer ring of permanent magnets 2314 a, amiddle ring of permanent magnets 2314 b, an inner ring of permanentmagnets 2314 c, and a permanent magnet disk 2314 d at the center. Thoughshown with four concentric permanent magnet rings, permanent magnet 2310b (and permanent magnet 2310 a) may have any suitable number ofpermanent magnet rings. Permanent magnet 2310 a may be formedsubstantially identically to permanent magnet 2310 b and, for example,comprise the same set of permanent magnet rings as permanent magnet 2310b.

As shown in FIG. 23A, yoke 2320 comprises a frame 2322 and plates 2324 aand 2324 b. Plates 2324 a and 2324 b may capture magnetic flux generatedby permanent magnets 2310 a and 2310 b and direct it to frame 2122 to becirculated via the magnetic return path of the yoke to increase the fluxdensity in the field of view of the B₀ magnet. Yoke 2320 may beconstructed of any desired ferromagnetic material, for example, lowcarbon steel, CoFe and/or silicon steel, etc. to provide the desiredmagnetic properties for the yoke.

FIGS. 24A and 24B illustrate views of a portable MRI system 2400, inaccordance with some embodiments of the technology described herein.Portable MRI system 2400 comprises a B₀ magnet 2410 formed in part by anupper magnet 2410 a and a lower magnet 2410 b having a yoke 2420 coupledthereto to increase the flux density within the imaging region. The B₀magnet 2410 may be housed in magnet housing 2412 along with gradientcoils 2415. The B₀ magnet 2410 may be the permanent magnet 2310 a and2310 b described with reference to FIG. 23 and/or any other suitabletype of magnet.

Illustrative portable MRI system 2400 further comprises a base 2450housing the electronics that operates the MRI system. For example, base2450 may house electronics including, but not limited to, one or moregradient power amplifiers, an on-system computer (e.g., including one ormore GPUs to perform neural network calculations in accordance with someembodiments of the technology described herein), a power distributionunit, one or more power supplies, and/or any other power componentsconfigured to operate the MRI system using mains electricity (e.g., viaa connection to a standard wall outlet and/or a large appliance outlet).For example, base 2470 may house low power components, such as thosedescribed herein, enabling at least in part the portable MRI system tobe powered from readily available wall outlets. Accordingly, portableMRI system 2400 can be brought to the patient and plugged into a walloutlet in his or her vicinity.

Portable MRI system 2400 further comprises moveable slides 2460 that canbe opened and closed and positioned in a variety of configurations.Slides 2460 include electromagnetic shielding 2465, which can be madefrom any suitable conductive or magnetic material, to form a moveableshield to attenuate electromagnetic noise in the operating environmentof the portable MRI system to shield the imaging region from at leastsome electromagnetic noise.

In portable MRI system 2400 illustrated in FIGS. 24A and 24B, themoveable shields are configurable to provide shielding in differentarrangements, which can be adjusted as needed to accommodate a patient,provide access to a patient, and/or in accordance with a given imagingprotocol. For example, for an imaging procedure such as a brain scan,once the patient has been positioned, slides 2460 can be closed, forexample, using handle 2462 to provide electromagnetic shielding 2465around the imaging region except for the opening that accommodates thepatient's upper torso. As another example, for an imaging procedure suchas a knee scan, slides 2460 may be arranged to have openings on bothsides to accommodate the patient's leg or legs. Accordingly, moveableshields allow the shielding to be configured in arrangements suitablefor the imaging procedure and to facilitate positioning the patientappropriately within the imaging region. Electrical gaskets may bearranged to provide continuous shielding along the periphery of themoveable shield. For example, as shown in FIG. 24B, electrical gaskets2467 a and 2467 b may be provided at the interface between slides 2460and magnet housing to maintain to provide continuous shielding alongthis interface. In some embodiments, the electrical gaskets areberyllium fingers or beryllium-copper fingers, or the like (e.g.,aluminum gaskets), that maintain electrical connection between shields2465 and ground during and after slides 2460 are moved to desiredpositions about the imaging region.

To facilitate transportation, a motorized component 2480 is provide toallow portable MRI system to be driven from location to location, forexample, using a control such as a joystick or other control mechanismprovided on or remote from the MRI system. In this manner, portable MRIsystem 2400 can be transported to the patient and maneuvered to thebedside to perform imaging.

FIG. 25A illustrates a portable MRI system 2500 that has beentransported to a patient's bedside to perform a brain scan. FIG. 25Billustrates portable MRI system 2500 that has been transported to apatient's bedside to perform a scan of the patient's knee. As shown inFIG. 25B, shielding 2565 includes shields 2560 having electrical gaskets2467 c.

FIG. 26 is a diagram of an illustrative computer system on whichembodiments described herein may be implemented. An illustrativeimplementation of a computer system 2600 that may be used in connectionwith any of the embodiments of the disclosure provided herein is shownin FIG. 26. For example, the processes described with reference to FIGS.2D, 8A-8B, 16, 20, and 21 may be implemented on and/or using computersystem 2600. As another example, the computer system 2600 may be used totrain and/or use any of the neural network statistical models describedherein. The computer system 2600 may include one or more processors 2610and one or more articles of manufacture that comprise non-transitorycomputer-readable storage media (e.g., memory 2620 and one or morenon-volatile storage media 2630). The processor 2610 may control writingdata to and reading data from the memory 2620 and the non-volatilestorage device 2630 in any suitable manner, as the aspects of thedisclosure provided herein are not limited in this respect. To performany of the functionality described herein, the processor 2610 mayexecute one or more processor-executable instructions stored in one ormore non-transitory computer-readable storage media (e.g., the memory2620), which may serve as non-transitory computer-readable storage mediastoring processor-executable instructions for execution by the processor2610.

Having thus described several aspects and embodiments of the technologyset forth in the disclosure, it is to be appreciated that variousalterations, modifications, and improvements will readily occur to thoseskilled in the art. Such alterations, modifications, and improvementsare intended to be within the spirit and scope of the technologydescribed herein. For example, those of ordinary skill in the art willreadily envision a variety of other means and/or structures forperforming the function and/or obtaining the results and/or one or moreof the advantages described herein, and each of such variations and/ormodifications is deemed to be within the scope of the embodimentsdescribed herein. Those skilled in the art will recognize, or be able toascertain using no more than routine experimentation, many equivalentsto the specific embodiments described herein. It is, therefore, to beunderstood that the foregoing embodiments are presented by way ofexample only and that, within the scope of the appended claims andequivalents thereto, inventive embodiments may be practiced otherwisethan as specifically described. In addition, any combination of two ormore features, systems, articles, materials, kits, and/or methodsdescribed herein, if such features, systems, articles, materials, kits,and/or methods are not mutually inconsistent, is included within thescope of the present disclosure.

The above-described embodiments can be implemented in any of numerousways. One or more aspects and embodiments of the present disclosureinvolving the performance of processes or methods may utilize programinstructions executable by a device (e.g., a computer, a processor, orother device) to perform, or control performance of, the processes ormethods. In this respect, various inventive concepts may be embodied asa computer readable storage medium (or multiple computer readablestorage media) (e.g., a computer memory, one or more floppy discs,compact discs, optical discs, magnetic tapes, flash memories, circuitconfigurations in Field Programmable Gate Arrays or other semiconductordevices, or other tangible computer storage medium) encoded with one ormore programs that, when executed on one or more computers or otherprocessors, perform methods that implement one or more of the variousembodiments described above. The computer readable medium or media canbe transportable, such that the program or programs stored thereon canbe loaded onto one or more different computers or other processors toimplement various ones of the aspects described above. In someembodiments, computer readable media may be non-transitory media.

The terms “program” or “software” are used herein in a generic sense torefer to any type of computer code or set of computer-executableinstructions that can be employed to program a computer or otherprocessor to implement various aspects as described above. Additionally,it should be appreciated that according to one aspect, one or morecomputer programs that when executed perform methods of the presentdisclosure need not reside on a single computer or processor, but may bedistributed in a modular fashion among a number of different computersor processors to implement various aspects of the present disclosure.

Computer-executable instructions may be in many forms, such as programmodules, executed by one or more computers or other devices. Generally,program modules include routines, programs, objects, components, datastructures, etc. that perform particular tasks or implement particularabstract data types. Typically the functionality of the program modulesmay be combined or distributed as desired in various embodiments.

Also, data structures may be stored in computer-readable media in anysuitable form. For simplicity of illustration, data structures may beshown to have fields that are related through location in the datastructure. Such relationships may likewise be achieved by assigningstorage for the fields with locations in a computer-readable medium thatconvey relationship between the fields. However, any suitable mechanismmay be used to establish a relationship between information in fields ofa data structure, including through the use of pointers, tags or othermechanisms that establish relationship between data elements.

When implemented in software, the software code can be executed on anysuitable processor or collection of processors, whether provided in asingle computer or distributed among multiple computers.

Further, it should be appreciated that a computer may be embodied in anyof a number of forms, such as a rack-mounted computer, a desktopcomputer, a laptop computer, or a tablet computer, as non-limitingexamples. Additionally, a computer may be embedded in a device notgenerally regarded as a computer but with suitable processingcapabilities, including a Personal Digital Assistant (PDA), a smartphoneor any other suitable portable or fixed electronic device.

Also, a computer may have one or more input and output devices. Thesedevices can be used, among other things, to present a user interface.Examples of output devices that can be used to provide a user interfaceinclude printers or display screens for visual presentation of outputand speakers or other sound generating devices for audible presentationof output. Examples of input devices that can be used for a userinterface include keyboards, and pointing devices, such as mice, touchpads, and digitizing tablets. As another example, a computer may receiveinput information through speech recognition or in other audibleformats.

Such computers may be interconnected by one or more networks in anysuitable form, including a local area network or a wide area network,such as an enterprise network, and intelligent network (IN) or theInternet. Such networks may be based on any suitable technology and mayoperate according to any suitable protocol and may include wirelessnetworks, wired networks or fiber optic networks.

Also, as described, some aspects may be embodied as one or more methods.The acts performed as part of the method may be ordered in any suitableway. Accordingly, embodiments may be constructed in which acts areperformed in an order different than illustrated, which may includeperforming some acts simultaneously, even though shown as sequentialacts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases. Multiple elements listed with“and/or” should be construed in the same fashion, i.e., “one or more” ofthe elements so conjoined. Other elements may optionally be presentother than the elements specifically identified by the “and/or” clause,whether related or unrelated to those elements specifically identified.Thus, as a non-limiting example, a reference to “A and/or B”, when usedin conjunction with open-ended language such as “comprising” can refer,in one embodiment, to A only (optionally including elements other thanB); in another embodiment, to B only (optionally including elementsother than A); in yet another embodiment, to both A and B (optionallyincluding other elements); etc.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified. Thus, as anon-limiting example, “at least one of A and B” (or, equivalently, “atleast one of A or B,” or, equivalently “at least one of A and/or B”) canrefer, in one embodiment, to at least one, optionally including morethan one, A, with no B present (and optionally including elements otherthan B); in another embodiment, to at least one, optionally includingmore than one, B, with no A present (and optionally including elementsother than A); in yet another embodiment, to at least one, optionallyincluding more than one, A, and at least one, optionally including morethan one, B (and optionally including other elements); etc.

In the claims, as well as in the specification above, all transitionalphrases such as “comprising,” “including,” “carrying,” “having,”“containing,” “involving,” “holding,” “composed of,” and the like are tobe understood to be open-ended, i.e., to mean including but not limitedto. Only the transitional phrases “consisting of” and “consistingessentially of” shall be closed or semi-closed transitional phrases,respectively.

The terms “approximately” and “about” may be used to mean within ±20% ofa target value in some embodiments, within ±10% of a target value insome embodiments, within ±5% of a target value in some embodiments,within ±2% of a target value in some embodiments. The terms“approximately” and “about” may include the target value.

What is claimed is:
 1. A method for generating magnetic resonance (MR)images of a subject from MR data obtained by a magnetic resonanceimaging (MRI) system, the method comprising: obtaining input MR spatialfrequency data obtained by imaging the subject using the MRI system;generating an MR image of the subject from the input MR spatialfrequency data using a neural network model comprising: apre-reconstruction neural network configured to process the input MRspatial frequency data; a reconstruction neural network configured togenerate at least one initial image of the subject from output of thepre-reconstruction neural network; and a post-reconstruction neuralnetwork configured to generate the MR image of the subject from the atleast one initial image of the subject.
 2. The method of claim 1,wherein the input MR spatial frequency data is under-sampled relative toa Nyquist criterion.
 3. The method of claim 1, wherein points in theinput MR spatial frequency data were obtained using a non-Cartesiansampling trajectory.
 4. The method of claim 1, wherein thepre-reconstruction neural network comprises a first neural networkconfigured to suppress RF interference, the first neural networkcomprising one or more convolutional layers.
 5. The method of claim 4,wherein the pre-reconstruction neural network comprises a second neuralnetwork configured to suppress noise, the second neural networkcomprising one or more convolutional layers.
 6. The method of claim 5,wherein the pre-reconstruction neural network comprises a third neuralnetwork configured to perform line rejection, the third neural networkcomprising one or more convolutional layers.
 7. The method of claim 1,wherein the reconstruction neural network was trained to reconstruct MRimages from spatial frequency MR data under-sampled relative to aNyquist criterion.
 8. The method of claim 1, wherein the reconstructionneural network is configured to perform data consistency processingusing a non-uniform Fourier transformation for transforming image datato spatial frequency data.
 9. The method of claim 8, wherein thereconstruction neural network is configured to perform data consistencyprocessing using the non-uniform Fourier transformation at least in partby applying the non-uniform Fourier transformation on data by applying ade-apodization transformation, a fast Fourier transformation, and agridding interpolation transformation to the data.
 10. The method ofclaim 1, wherein the MRI system comprises a plurality of RF coils;wherein the at least one initial image of the subject comprises aplurality of images, each of the plurality of images generated from aportion of the input MR spatial frequency data collected by a respectiveRF coil in a plurality of RF coils; wherein the post-reconstructionneural network comprises a first neural network configured to estimate aplurality of RF coil profiles corresponding to the plurality of RFcoils, the method further comprising: generating the MR image of thesubject using the plurality of MR images and the plurality of RF coilprofiles.
 11. The method of claim 1, wherein the at least one initialimage of the subject comprises a first set of one or more MR images anda second set of one or more MR images, and wherein thepost-reconstruction neural network comprises a second neural network foraligning the first set of MR images to the second set of MR images. 12.The method of claim 1, wherein the post-reconstruction neural networkcomprises a neural network configured to suppress noise in the at leastone initial image and/or at least one image obtained from the at leastone initial image.
 13. The method of claim 1, wherein thepre-reconstruction neural network, the reconstruction neural network,and the post-reconstruction neural network are jointly trained withrespect to a common loss function.
 14. The method of claim 13, where thecommon loss function is a weighted combination of a first loss functionfor the pre-reconstruction neural network, a second loss function forthe reconstruction neural network, and a third loss function for thepost-reconstruction neural network.
 15. A magnetic resonance imaging(MRI) system, comprising: a magnetics system having a plurality ofmagnetics components to produce magnetic fields for performing MRI; andat least one processor configured to perform: obtaining input MR spatialfrequency data obtained by imaging the subject using the MRI system;generating an MR image of the subject from the input MR spatialfrequency data using a neural network model comprising: apre-reconstruction neural network configured to process the input MRspatial frequency data; a reconstruction neural network configured togenerate at least one initial image of the subject from output of thepre-reconstruction neural network; and a post-reconstruction neuralnetwork configured to generate the MR image of the subject from the atleast one initial image of the subject.
 16. The MRI system of claim 15,wherein the magnetics system comprises a permanent B₀ magnet configuredto generate a B₀ magnetic field.
 17. The MRI system of claim 16, whereinthe B₀ magnet comprises a plurality of concentric permanent magnetrings.
 18. The MRI system of claim 15, wherein the plurality ofmagnetics components include at least one permanent B₀ magnet configuredto produce a B₀ field for an imaging region of the MRI system, the B₀field having a strength between 50 milliTesla and 100 milliTesla. 19.The MRI system of claim 15, wherein the plurality of magneticscomponents include at least one gradient coil.
 20. At least onenon-transitory computer readable storage medium storingprocessor-executable instructions that, when executed by at least oneprocessor, cause the at least one processor to perform a method forgenerating magnetic resonance (MR) images of a subject from MR dataobtained by a magnetic resonance imaging (MRI) system, the methodcomprising: obtaining input MR spatial frequency data obtained byimaging the subject using the MRI system; generating an MR image of thesubject from the input MR spatial frequency data using a neural networkmodel comprising: a pre-reconstruction neural network configured toprocess the input MR spatial frequency data; a reconstruction neuralnetwork configured to generate at least one initial image of the subjectfrom output of the pre-reconstruction neural network; and apost-reconstruction neural network configured to generate the MR imageof the subject from the at least one initial image of the subject.